Fun with Algorithms最新文献_第2页

How long does it take for all users in a social network to choose their communities? 一个社交网络的所有用户选择他们的社区需要多长时间?

Fun with Algorithms Pub Date : 2019-11-01 DOI: 10.4230/LIPIcs.FUN.2018.6

J. Bermond, A. Chaintreau, G. Ducoffe, Dorian Mazauric

{"title":"How long does it take for all users in a social network to choose their communities?","authors":"J. Bermond, A. Chaintreau, G. Ducoffe, Dorian Mazauric","doi":"10.4230/LIPIcs.FUN.2018.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2018.6","url":null,"abstract":"We consider a community formation problem in social networks, where the users are either friends or enemies. The users are partitioned into conflict-free groups (i.e., independent sets in the conflict graph $G^- =(V,E)$ that represents the enmities between users). The dynamics goes on as long as there exists any set of at most k users, k being any fixed parameter, that can change their current groups in the partition simultaneously, in such a way that they all strictly increase their utilities (number of friends i.e., the cardinality of their respective groups minus one). \u0000Previously, the best-known upper-bounds on the maximum time of convergence were $O(|V|alpha(G^-))$ for k $leq 2$ and $O(|V|^3) for k=3$, with $alpha(G^-)$ being the independence number of $G^-$. Our first contribution in this paper consists in reinterpreting the initial problem as the study of a dominance ordering over the vectors of integer partitions. With this approach, we obtain for $k leq 2$ the tight upper-bound $O(|V| min{ alpha(G^-)$, $sqrt{|V|} })$ and, when $G^-$ is the empty graph, the exact value of order $frac{(2|V|)^{3/2}}{3}$. \u0000The time of convergence, for any fixed k geq 4, was conjectured to be polynomial. In this paper we disprove this. Specifically, we prove that for any k geq 4, the maximum time of convergence is an $Omega(|V|^{Theta(log{|V|})})$.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123928469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Taming the Knight's Tour: Minimizing Turns and Crossings 驯服骑士之旅:减少转弯和交叉

Fun with Algorithms Pub Date : 2019-04-04 DOI: 10.4230/LIPIcs.FUN.2021.4

Juan José Besa Vial, Timothy Johnson, Nil Mamano, Martha C. Osegueda

引用次数: 0

A Cryptographer's Conspiracy Santa 密码学家的阴谋圣诞老人

Fun with Algorithms Pub Date : 2018-06-13 DOI: 10.4230/LIPIcs.FUN.2018.13

Xavier Bultel, Jannik Dreier, J. Dumas, P. Lafourcade

{"title":"A Cryptographer's Conspiracy Santa","authors":"Xavier Bultel, Jannik Dreier, J. Dumas, P. Lafourcade","doi":"10.4230/LIPIcs.FUN.2018.13","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2018.13","url":null,"abstract":"In Conspiracy Santa, a variant of Secret Santa, a group of people offer each other Christmas gifts, where each member of the group receives a gift from the other members of the group. To that end, the members of the group form conspiracies, to decide on appropriate gifts, and usually divide the cost of each gift among all participants of that conspiracy. This requires to settle the shared expenses per conspiracy, so Conspiracy Santa can actually be seen as an aggregation of several shared expenses problems. First, we show that the problem of finding a minimal number of transaction when settling shared expenses is NP-complete. Still, there exists good greedy approximations. Second, we present a greedy distributed secure solution to Conspiracy Santa. This solution allows a group of people to share the expenses for the gifts in such a way that no participant learns the price of his gift, but at the same time notably reduces the number of transactions with respect to a naive aggregation. Furthermore, our solution does not require a trusted third party, and can either be implemented physically (the participants are in the same room and exchange money using envelopes) or, virtually, using a cryptocurrency.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129028206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

SUPERSET: A (Super)Natural Variant of the Card Game SET 超集:卡牌游戏集的(超级)自然变体

Fun with Algorithms Pub Date : 2018-06-01 DOI: 10.4230/LIPIcs.FUN.2018.12

F. Botler, Andrés Cristi, R. Hoeksma, Kevin Schewior, Andreas Tönnis

引用次数: 0

Restricted Power - Computational Complexity Results for Strategic Defense Games 有限力量——战略防御博弈的计算复杂性结果

Fun with Algorithms Pub Date : 2018-06-01 DOI: 10.4230/LIPIcs.FUN.2018.17

Ronald de Haan, Petra Wolf

引用次数: 2

Tracks from hell - when finding a proof may be easier than checking it 来自地狱的踪迹——当找到一个证明可能比检查它更容易

Fun with Algorithms Pub Date : 2018-05-25 DOI: 10.4230/LIPIcs.FUN.2018.4

Matteo Almanza, S. Leucci, A. Panconesi

引用次数: 2

Kings, Name Days, Lazy Servants and Magic 国王，命名日，懒惰的仆人和魔法

Fun with Algorithms Pub Date : 2018-05-25 DOI: 10.4230/LIPIcs.FUN.2018.10

P. Boldi, S. Vigna

{"title":"Kings, Name Days, Lazy Servants and Magic","authors":"P. Boldi, S. Vigna","doi":"10.4230/LIPIcs.FUN.2018.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2018.10","url":null,"abstract":"Once upon a time, a king had a very, very long list of names of his subjects. The king was also a bit obsessed with name days: every day he would ask his servants to look the list for all persons having their name day. Reading every day the whole list was taking an enormous amount of time to the king's servants. One day, the chancellor had a magnificent idea: he wrote a book with instructions. The number of pages in the book was equal to the number of names, but following the instructions one could find all people having their name day by looking at only a few pages - in fact, as many pages as the length of the name - and just glimpsing at the list. Everybody was happy, but in time the king's servants got lazy: when the name was very long they would find excuses to avoid looking at so many pages, and some name days were skipped. Desperate, the king made a call through its reign, and a fat sorceress answered. There was a way to look at much, much fewer pages using an additional magic book. But sometimes, very rarely, it would not work (magic does not always work). The king accepted the offer, and name days parties restarted. Only, once every a few thousand years, the magic book fails, and the assistants have to go by the chancellor book. So the parties start a bit later. But they start anyway.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116542033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible 谁见证了见证者?在《见证者》中寻找证人很难，有时甚至是不可能的

Fun with Algorithms Pub Date : 2018-04-26 DOI: 10.4230/LIPIcs.FUN.2018.3

Zachary Abel, Jeffrey Bosboom, E. Demaine, Linus Hamilton, Adam Hesterberg, Justin Kopinsky, J. Lynch, Mikhail Rudoy

{"title":"Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible","authors":"Zachary Abel, Jeffrey Bosboom, E. Demaine, Linus Hamilton, Adam Hesterberg, Justin Kopinsky, J. Lynch, Mikhail Rudoy","doi":"10.4230/LIPIcs.FUN.2018.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2018.3","url":null,"abstract":"We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some edges or vertices to be visited (hexagons); forcing some cells to have certain numbers of incident path edges (triangles); or forcing the regions formed by the path to be partially monochromatic (squares), have exactly two special cells (stars), or be singly covered by given shapes (polyominoes) and/or negatively counting shapes (antipolyominoes). We show that any one of these clue types (except the first) is enough to make path finding NP-complete (\"witnesses exist but are hard to find\"), even for rectangular boards. Furthermore, we show that a final clue type (antibody), which necessarily \"cancels\" the effect of another clue in the same region, makes path finding Sigma_2-complete (\"witnesses do not exist\"), even with a single antibody (combined with many anti/polyominoes), and the problem gets no harder with many antibodies.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124970295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Algorithms and Insights for RaceTrack RaceTrack的算法和见解

Fun with Algorithms Pub Date : 2018-04-24 DOI: 10.4230/LIPIcs.FUN.2016.6

M. Bekos, Till Bruckdorfer, Henry Förster, M. Kaufmann, Simon Poschenrieder, Thomas Stüber

引用次数: 3

Faster Evaluation of Subtraction Games 快速评估减法游戏

Fun with Algorithms Pub Date : 2018-04-18 DOI: 10.4230/LIPIcs.FUN.2018.20

D. Eppstein

{"title":"Faster Evaluation of Subtraction Games","authors":"D. Eppstein","doi":"10.4230/LIPIcs.FUN.2018.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2018.20","url":null,"abstract":"Subtraction games are played with one or more heaps of tokens, with players taking turns removing from a single heap a number of tokens belonging to a specified subtraction set; the last player to move wins. We describe how to compute the set of winning heap sizes in single-heap subtraction games (for an input consisting of the subtraction set and maximum heap size $n$), in time $tilde O(n)$, where the $tilde O$ elides logarithmic factors. For multi-heap games, the optimal game play is determined by the nim-value of each heap; we describe how to compute the nim-values of all heaps of size up to~$n$ in time $tilde O(mn)$, where $m$ is the maximum nim-value occurring among these heap sizes. These time bounds improve naive dynamic programming algorithms with time $O(n|S|)$, because $mle|S|$ for all such games. We apply these results to the game of subtract-a-square, whose set of winning positions is a maximal square-difference-free set of a type studied in number theory in connection with the Furstenberg-Sarkozy theorem. We provide experimental evidence that, for this game, the set of winning positions has a density comparable to that of the densest known square-difference-free sets, and has a modular structure related to the known constructions for these dense sets. Additionally, this game's nim-values are (experimentally) significantly smaller than the size of its subtraction set, implying that our algorithm achieves a polynomial speedup over dynamic programming.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129013366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1