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Square-Triangle Tilings: Lift & Flip to Sample? 正方形-三角形天花板：举起并翻转以取样？
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-24 DOI: arxiv-2406.16402
Thomas FerniqueHSE, Moscow, Russia, Olga Mikhailovna SizovaSemenov Institute of Chemical Physics, Moscow, Russia
{"title":"Square-Triangle Tilings: Lift & Flip to Sample?","authors":"Thomas FerniqueHSE, Moscow, Russia, Olga Mikhailovna SizovaSemenov Institute of Chemical Physics, Moscow, Russia","doi":"arxiv-2406.16402","DOIUrl":"https://doi.org/arxiv-2406.16402","url":null,"abstract":"We introduce an elementary transformation called flips on tilings by squares\u0000and triangles and conjecture that it connects any two tilings of the same\u0000region of the Euclidean plane.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"210 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526089","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
Pop Stacks with a Bypass 带旁路的弹出堆栈
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-24 DOI: arxiv-2406.16399
Lapo CioniUniversity of Pisa, Italy, Luca FerrariUniversity of Firenze, Italy, Rebecca SmithSUNY Brockport
{"title":"Pop Stacks with a Bypass","authors":"Lapo CioniUniversity of Pisa, Italy, Luca FerrariUniversity of Firenze, Italy, Rebecca SmithSUNY Brockport","doi":"arxiv-2406.16399","DOIUrl":"https://doi.org/arxiv-2406.16399","url":null,"abstract":"We consider sorting procedures for permutations making use of pop stacks with\u0000a bypass operation, and explore the combinatorial properties of the associated\u0000algorithms.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526088","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
On the Confluence of Directed Graph Reductions Preserving Feedback Vertex Set Minimality 论保持反馈顶点集最小性的有向图演绎的汇合点
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-24 DOI: arxiv-2406.16390
Moussa Abdenbi, Alexandre Blondin Massé, Alain Goupil, Odile Marcotte
{"title":"On the Confluence of Directed Graph Reductions Preserving Feedback Vertex Set Minimality","authors":"Moussa Abdenbi, Alexandre Blondin Massé, Alain Goupil, Odile Marcotte","doi":"arxiv-2406.16390","DOIUrl":"https://doi.org/arxiv-2406.16390","url":null,"abstract":"In graph theory, the minimum directed feedback vertex set (FVS) problem\u0000consists in identifying the smallest subsets of vertices in a directed graph\u0000whose deletion renders the directed graph acyclic. Although being known as\u0000NP-hard since 1972, this problem can be solved in a reasonable time on small\u0000instances, or on instances having special combinatorial structure. In this\u0000paper we investigate graph reductions preserving all or some minimum FVS and\u0000focus on their properties, especially the Church-Rosser property, also called\u0000confluence. The Church-Rosser property implies the irrelevance of reduction\u0000order, leading to a unique directed graph. The study seeks the largest subset\u0000of reductions with the Church-Rosser property and explores the adaptability of\u0000reductions to meet this criterion. Addressing these questions is crucial, as it\u0000may impact algorithmic implications, allowing for parallelization and speeding\u0000up sequential algorithms.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526094","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
Database for identifiability properties of linear compartmental models 线性区室模型可识别性数据库
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-23 DOI: arxiv-2406.16132
Natali Gogishvili
{"title":"Database for identifiability properties of linear compartmental models","authors":"Natali Gogishvili","doi":"arxiv-2406.16132","DOIUrl":"https://doi.org/arxiv-2406.16132","url":null,"abstract":"Structural identifiability is an important property of parametric ODE models.\u0000When conducting an experiment and inferring the parameter value from the\u0000time-series data, we want to know if the value is globally, locally, or\u0000non-identifiable. Global identifiability of the parameter indicates that there\u0000exists only one possible solution to the inference problem, local\u0000identifiability suggests that there could be several (but finitely many)\u0000possibilities, while non-identifiability implies that there are infinitely many\u0000possibilities for the value. Having this information is useful since, one\u0000would, for example, only perform inferences for the parameters which are\u0000identifiable. Given the current significance and widespread research conducted\u0000in this area, we decided to create a database of linear compartment models and\u0000their identifiability results. This facilitates the process of checking\u0000theorems and conjectures and drawing conclusions on identifiability. By only\u0000storing models up to symmetries and isomorphisms, we optimize memory efficiency\u0000and reduce query time. We conclude by applying our database to real problems.\u0000We tested a conjecture about deleting one leak of the model states in the paper\u0000'Linear compartmental models: Input-output equations and operations that\u0000preserve identifiability' by E. Gross et al., and managed to produce a\u0000counterexample. We also compute some interesting statistics related to the\u0000identifiability of linear compartment model parameters.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526100","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
Exponential Time Approximation for Coloring 3-Colorable Graphs 三色图着色的指数时间近似法
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-21 DOI: arxiv-2406.15563
Venkatesan Guruswami, Rhea Jain
{"title":"Exponential Time Approximation for Coloring 3-Colorable Graphs","authors":"Venkatesan Guruswami, Rhea Jain","doi":"arxiv-2406.15563","DOIUrl":"https://doi.org/arxiv-2406.15563","url":null,"abstract":"The problem of efficiently coloring $3$-colorable graphs with few colors has\u0000received much attention on both the algorithmic and inapproximability fronts.\u0000We consider exponential time approximations, in which given a parameter $r$, we\u0000aim to develop an $r$-approximation algorithm with the best possible runtime,\u0000providing a tradeoff between runtime and approximation ratio. In this vein, an\u0000algorithm to $O(n^varepsilon)$-color a 3-colorable graphs in time\u0000$2^{Theta(n^{1-2varepsilon}log(n))}$ is given in (Atserias and Dalmau, SODA\u00002022.) We build on tools developed in (Bansal et al., Algorithmic, 2019) to obtain\u0000an algorithm to color $3$-colorable graphs with $O(r)$ colors in\u0000$expleft(tilde{O}left(frac {nlog^{11/2}r} {r^3}right)right)$ time,\u0000asymptotically improving upon the bound given by Atserias and Dalmau.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526093","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
NP-Completeness of the Combinatorial Distance Matrix Realisation Problem 组合距离矩阵实现问题的 NP 完备性
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-20 DOI: arxiv-2406.14729
David L. Fairbairn, George B. Mertzios, Norbert Peyerimhoff
{"title":"NP-Completeness of the Combinatorial Distance Matrix Realisation Problem","authors":"David L. Fairbairn, George B. Mertzios, Norbert Peyerimhoff","doi":"arxiv-2406.14729","DOIUrl":"https://doi.org/arxiv-2406.14729","url":null,"abstract":"The $k$-CombDMR problem is that of determining whether an $n times n$\u0000distance matrix can be realised by $n$ vertices in some undirected graph with\u0000$n + k$ vertices. This problem has a simple solution in the case $k=0$. In this\u0000paper we show that this problem is polynomial time solvable for $k=1$ and\u0000$k=2$. Moreover, we provide algorithms to construct such graph realisations by\u0000solving appropriate 2-SAT instances. In the case where $k geq 3$, this problem\u0000is NP-complete. We show this by a reduction of the $k$-colourability problem to\u0000the $k$-CombDMR problem. Finally, we discuss the simpler polynomial time\u0000solvable problem of tree realisability for a given distance matrix.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526095","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
An Algorithm for the Assignment Game Beyond Additive Valuations 超越加法估值的分配博弈算法
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-19 DOI: arxiv-2406.13620
Eric Balkanski, Christopher En, Yuri Faenza
{"title":"An Algorithm for the Assignment Game Beyond Additive Valuations","authors":"Eric Balkanski, Christopher En, Yuri Faenza","doi":"arxiv-2406.13620","DOIUrl":"https://doi.org/arxiv-2406.13620","url":null,"abstract":"The assignment game, introduced by Shapley and Shubik (1971), is a classic\u0000model for two-sided matching markets between buyers and sellers. In the\u0000original assignment game, it is assumed that payments lead to transferable\u0000utility and that buyers have unit-demand valuations for the items being sold.\u0000Two important and mostly independent lines of work have studied more general\u0000settings with imperfectly transferable utility and gross substitutes\u0000valuations. Multiple efficient algorithms have been proposed for computing a\u0000competitive equilibrium, the standard solution concept in assignment games, in\u0000these two settings. Our main result is an efficient algorithm for computing\u0000competitive equilibria in a setting with both imperfectly transferable utility\u0000and gross substitutes valuations. Our algorithm combines augmenting path\u0000techniques from maximum matching and algorithms for matroid intersection. We\u0000also show that, in a mild generalization of our model, computing a competitive\u0000equilibrium is NP-hard.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507054","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
Proceedings of the 13th edition of the conference on Random Generation of Combinatorial Structures. Polyominoes and Tilings 第 13 届组合结构随机生成会议论文集。多面体与叠层
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-19 DOI: arxiv-2406.14588
Srečko Brlek, Luca Ferrari
{"title":"Proceedings of the 13th edition of the conference on Random Generation of Combinatorial Structures. Polyominoes and Tilings","authors":"Srečko Brlek, Luca Ferrari","doi":"arxiv-2406.14588","DOIUrl":"https://doi.org/arxiv-2406.14588","url":null,"abstract":"The conference GASCom brings together researchers in combinatorics,\u0000algorithms, probabilities, and more generally mathematical computer science,\u0000around the theme of random and exhaustive generation of combinatorial\u0000structures, mostly considered from a theoretical point of view. In connection\u0000with this main theme, the conference is also interested in contributions in\u0000enumerative or analytic combinatorics, and interactions with other areas of\u0000mathematics, computer science, physics or biology. The conference is both\u0000interested in methods for random or exhaustive generation and in original\u0000results on combinatorial or algorithmic questions, whose solution has been made\u0000possible by an approach involving random or exhaustive generation. The present\u0000edition of the conference includes a specific bunch of talks dedicated to\u0000polyominoes and tilings. A (not exhaustive) list of topics of the conference is: random and exhaustive\u0000generation of combinatorial objects; tilings and polyominoes; bijective,\u0000enumerative, algebraic and analytic combinatorics; algorithmic aspects:\u0000analysis of algorithms, probabilistic algorithms; interactions:\u0000bio-informatics, combinatorics on words, number theory.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532102","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
Pushing the Frontier on Approximate EFX Allocations 推动近似外频分配的前沿发展
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-18 DOI: arxiv-2406.12413
Georgios Amanatidis, Aris Filos-Ratsikas, Alkmini Sgouritsa
{"title":"Pushing the Frontier on Approximate EFX Allocations","authors":"Georgios Amanatidis, Aris Filos-Ratsikas, Alkmini Sgouritsa","doi":"arxiv-2406.12413","DOIUrl":"https://doi.org/arxiv-2406.12413","url":null,"abstract":"We study the problem of allocating a set of indivisible goods to a set of\u0000agents with additive valuation functions, aiming to achieve approximate\u0000envy-freeness up to any good ($alpha$-EFX). The state-of-the-art results on\u0000the problem include that (exact) EFX allocations exist when (a) there are at\u0000most three agents, or (b) the agents' valuation functions can take at most two\u0000values, or (c) the agents' valuation functions can be represented via a graph.\u0000For $alpha$-EFX, it is known that a $0.618$-EFX allocation exists for any\u0000number of agents with additive valuation functions. In this paper, we show that\u0000$2/3$-EFX allocations exist when (a) there are at most emph{seven agents}, (b)\u0000the agents' valuation functions can take at most emph{three values}, or (c)\u0000the agents' valuation functions can be represented via a emph{multigraph}. Our\u0000results can be interpreted in two ways. First, by relaxing the notion of EFX to\u0000$2/3$-EFX, we obtain existence results for strict generalizations of the\u0000settings for which exact EFX allocations are known to exist. Secondly, by\u0000imposing restrictions on the setting, we manage to beat the barrier of $0.618$\u0000and achieve an approximation guarantee of $2/3$. Therefore, our results push\u0000the emph{frontier} of existence and computation of approximate EFX\u0000allocations, and provide insights into the challenges of settling the existence\u0000of exact EFX allocations.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526099","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
On the maximal L1 influence of real-valued boolean functions 关于实值布尔函数的最大 L1 影响
arXiv - CS - Discrete Mathematics Pub Date : 2024-06-16 DOI: arxiv-2406.10772
Andrew J. Young, Henry D. Pfister
{"title":"On the maximal L1 influence of real-valued boolean functions","authors":"Andrew J. Young, Henry D. Pfister","doi":"arxiv-2406.10772","DOIUrl":"https://doi.org/arxiv-2406.10772","url":null,"abstract":"We show that any sequence of well-behaved (e.g. bounded and non-constant)\u0000real-valued functions of $n$ boolean variables ${f_n}$ admits a sequence of\u0000coordinates whose $L^1$ influence under the $p$-biased distribution, for any\u0000$pin(0,1)$, is $Omega(text{var}(f_n) frac{ln n}{n})$.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"346 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507059","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
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