This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013) (format=pdflatex 2013.5.30) 19 FEB 2014 20:53 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. %&-line parsing enabled. **algorithms.tex (./algorithms.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. ./algorithms.tex:4: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4 W e will say that a policy is non-adaptive if it selects a set of nodes $... ? Missing character: There is no W in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! 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Overfull \hbox (20.0pt too wide) in paragraph at lines 4--10 [] [] Overfull \hbox (17.26382pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^R [] Overfull \hbox (9.06943pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 X$ [] Overfull \hbox (6.06941pt too wide) in paragraph at lines 4--10 []$ [] Overfull \hbox (5.72458pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 u$ [] Overfull \hbox (6.70831pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 S$ [] Overfull \hbox (9.69218pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 q[]$ [] Overfull \hbox (20.04169pt too wide) in paragraph at lines 4--10 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 S\OMS/cmsy/m/n/10 j \OT1/cmr/m/n/10 + [] Overfull \hbox (29.31343pt too wide) in paragraph at lines 4--10 [][][] \OMS/cmsy/m/n/10 ^^T [] Overfull \hbox (5.52084pt too wide) in paragraph at lines 4--10 \OML/cmm/m/it/10 k$ [] ./algorithms.tex:11: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.11 \begin{equation} \label{eq:relaxed} ? Overfull \hbox (20.0pt too wide) in paragraph at lines 11--11 [] [] ./algorithms.tex:12: LaTeX Error: Environment split undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.12 \begin{split} ? ./algorithms.tex:14: Undefined control sequence. l.14 \max_{\substack {S\subseteq X\\q\in[0,1]^n} }& \; ? ./algorithms.tex:14: Misplaced alignment tab character &. l.14 ...x_{\substack{S\subseteq X\\q\in[0,1]^n} }& \; ? ./algorithms.tex:15: Undefined control sequence. l.15 \sum_{R\subseteq\neigh {X}}\textbf{p}\odot\textbf{q}_Rf(R)\\ ? ./algorithms.tex:16: Undefined control sequence. \text l.16 \text {s.t. } & \; |S|+\textbf{p}^T\textbf{q} \leq k,\; ? ./algorithms.tex:16: Misplaced alignment tab character &. l.16 \text{s.t. } & \; |S|+\textbf{p}^T\textbf{q} \leq k,\; ? ./algorithms.tex:17: Undefined control sequence. l.17 q_u \leq \mathbf{1}_{\{u\in\neigh {S}\}} ? ./algorithms.tex:18: LaTeX Error: \begin{equation} on input line 11 ended by \e nd{split}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.18 \end{split} ? Overfull \hbox (255.8566pt too wide) detected at line 19 [][] [] [] \OMS/cmsy/m/n/10 ^^L [][]\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cm m/m/it/10 R\OT1/cmr/m/n/10 )[] [] \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 S\OMS/cmsy /m/n/10 j \OT1/cmr/m/n/10 + [][][] \OMS/cmsy/m/n/10 ^^T \OML/cmm/m/it/10 k; q[ ] \OMS/cmsy/m/n/10 ^^T \OT1/cmr/bx/n/10 1[] [] ./algorithms.tex:21: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.21 w here $n\defeq|\neigh{X}|$,$\textbf{p}\odot \textbf{q}$ denotes compone... ? Missing character: There is no w in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! ./algorithms.tex:21: Undefined control sequence. l.21 where $n\defeq |\neigh{X}|$,$\textbf{p}\odot \textbf{q}$ denotes compone... ? ./algorithms.tex:21: Undefined control sequence. l.21 where $n\defeq|\neigh {X}|$,$\textbf{p}\odot \textbf{q}$ denotes compone... ? Missing character: There is no , in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 21--22 [] [] Overfull \hbox (34.794pt too wide) in paragraph at lines 21--22 \OML/cmm/m/it/10 n\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j$$[] ^^ L [] Overfull \hbox (6.06941pt too wide) in paragraph at lines 21--22 []$ [] Overfull \hbox (12.6295pt too wide) in paragraph at lines 21--22 [][]$ [] Overfull \hbox (6.06941pt too wide) in paragraph at lines 21--22 []$ [] Overfull \hbox (7.67015pt too wide) in paragraph at lines 21--22 \OML/cmm/m/it/10 R$ [] ./algorithms.tex:23: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.23 \begin{displaymath} ? Overfull \hbox (20.0pt too wide) in paragraph at lines 23--23 [][] [] ./algorithms.tex:24: Undefined control sequence. l.24 \txtbf {p}\circ \textbf{q}_R = \prod_{u\in R} p_uq_u\prod_{u\in\neig... ? ./algorithms.tex:24: Undefined control sequence. l.24 ...R = \prod_{u\in R} p_uq_u\prod_{u\in\neigh {X}\setminus ? Overfull \hbox (143.33928pt too wide) detected at line 26 \OML/cmm/m/it/10 p \OMS/cmsy/m/n/10 ^^N [][] \OT1/cmr/m/n/10 = [] \OML/cmm/m/it /10 p[]q[] []\OT1/cmr/m/n/10 (1 \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 p[]q[]\OT 1/cmr/m/n/10 ) [] ./algorithms.tex:28: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.28 N ote that because of the condition $q_u\leq \mathbf{1}_{\{u\in\neigh{S}... ? Missing character: There is no N in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! ./algorithms.tex:28: Undefined control sequence. l.28 ...ondition $q_u\leq \mathbf{1}_{\{u\in\neigh {S}\}}$, ? Missing character: There is no , in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! ./algorithms.tex:30: Undefined control sequence. \neigh l.30 $\neigh {X}\setminus\neigh{S}$. Hence, the summation in \eqref{eq:relaxe... ? ./algorithms.tex:30: Undefined control sequence. l.30 $\neigh{X}\setminus\neigh {S}$. Hence, the summation in \eqref{eq:relaxe... ? Missing character: There is no . in font nullfont! Missing character: There is no H in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! ./algorithms.tex:30: Undefined control sequence. l.30 ...\neigh{S}$. Hence, the summation in \eqref {eq:relaxed} is ? Missing character: There is no e in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no x in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no o in font nullfont! ./algorithms.tex:31: Undefined control sequence. l.31 restricted to $R\subseteq\neigh {S}$ as in \eqref{eq:problem}. ? Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! ./algorithms.tex:31: Undefined control sequence. l.31 ...cted to $R\subseteq\neigh{S}$ as in \eqref {eq:problem}. ? Missing character: There is no e in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no . in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 28--32 [] [] Overfull \hbox (20.2477pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 q[] \OMS/cmsy/m/n/10 ^^T [] Overfull \hbox (29.85446pt too wide) in paragraph at lines 28--32 \OT1/cmr/bx/n/10 1[]$ [] Overfull \hbox (10.03127pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 p \OMS/cmsy/m/n/10 ^^N [] Overfull \hbox (21.57973pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 q[] \OT1/cmr/m/n/10 = [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 28--32 \OT1/cmr/m/n/10 0$ [] Overfull \hbox (7.67015pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 R$ [] Overfull \hbox (14.06944pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 X \OMS/cmsy/m/n/10 n [] Overfull \hbox (6.70831pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 S$ [] Overfull \hbox (18.22566pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 R \OMS/cmsy/m/n/10 ^^R [] Overfull \hbox (6.70831pt too wide) in paragraph at lines 28--32 \OML/cmm/m/it/10 S$ [] ./algorithms.tex:60: Undefined control sequence. l.60 \subsection {Adaptivity gap for additive functions} ? ./algorithms.tex:60: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.60 \subsection{A daptivity gap for additive functions} ? Missing character: There is no A in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no W in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no j in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no . in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 60--62 [] [] ./algorithms.tex:63: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.63 t his form of non-adap ? Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no W in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no k in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no . in font nullfont! Missing character: There is no F in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no . in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 63--67 [] [] Overfull \hbox (33.38863pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 relaxed- [] Overfull \hbox (16.35547pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 non [] Overfull \hbox (24.02208pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 adap- [] Overfull \hbox (15.58876pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 tive [] Overfull \hbox (18.91098pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 poli- [] Overfull \hbox (16.35544pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 cies [] Overfull \hbox (13.41655pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 are [] Overfull \hbox (35.26639pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 stronger [] Overfull \hbox (19.16655pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 than [] Overfull \hbox (19.93321pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 non- [] Overfull \hbox (36.0331pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 adaptive [] Overfull \hbox (18.91098pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 poli- [] Overfull \hbox (16.35544pt too wide) in paragraph at lines 63--67 \OT1/cmr/m/it/10 cies [] ./algorithms.tex:69: LaTeX Error: Environment proposition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.69 \begin{proposition} \label{prop:gap} ? ./algorithms.tex:70: LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.70 F or additive functions of the form given by \eqref{eq:voter}, non-a... ? Missing character: There is no F in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no y in font nullfont! ./algorithms.tex:70: Undefined control sequence. l.70 ...tive functions of the form given by \eqref {eq:voter}, non-adaptive ? Missing character: There is no e in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font n