SIAM Journal on Discrete Mathematics最新文献_第3页

A Simple Proof of the Nonuniform Kahn–Kalai Conjecture 非均匀卡恩-卡莱猜想的简单证明

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-04 DOI: 10.1137/23m1587075

Bryan Park, Jan Vondrák

引用次数: 0

Simple Algorithms for Stochastic Score Classification with Small Approximation Ratios 小近似比随机分数分类的简单算法

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-04 DOI: 10.1137/22m1523492

Benedikt M. Plank, Kevin Schewior

{"title":"Simple Algorithms for Stochastic Score Classification with Small Approximation Ratios","authors":"Benedikt M. Plank, Kevin Schewior","doi":"10.1137/22m1523492","DOIUrl":"https://doi.org/10.1137/22m1523492","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2069-2088, September 2024. <br/> Abstract. We revisit the Stochastic Score Classification (SSC) problem introduced by Gkenosis et al. (ESA 2018): We are given [math] tests. Each test [math] can be conducted at cost [math], and it succeeds independently with probability [math]. Further, a partition of the (integer) interval [math] into [math] smaller intervals is known. The goal is to conduct tests so as to determine that interval from the partition in which the number of successful tests lies while minimizing the expected cost. Ghuge, Gupta, and Nagarajan (IPCO 2022) recently showed that a polynomial-time constant-factor approximation algorithm exists. We show that interweaving the two strategies that order tests increasingly by their [math] and [math] ratios, respectively—as already proposed by Gkensosis et al. for a special case—yields a small approximation ratio. We also show that the approximation ratio can be slightly decreased from 6 to [math] by adding in a third strategy that simply orders tests increasingly by their costs. The similar analyses for both algorithms are nontrivial but arguably clean. Finally, we complement the implied upper bound of [math] on the adaptivity gap with a lower bound of 3/2. Since the lower-bound instance is a so-called unit-cost [math]-of-[math] instance, we settle the adaptivity gap in this case.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Functors on Relational Structures Which Admit Both Left and Right Adjoints 关系结构上既允许左相接又允许右相接的函数

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-03 DOI: 10.1137/23m1555223

Víctor Dalmau, Andrei Krokhin, Jakub Opršal

{"title":"Functors on Relational Structures Which Admit Both Left and Right Adjoints","authors":"Víctor Dalmau, Andrei Krokhin, Jakub Opršal","doi":"10.1137/23m1555223","DOIUrl":"https://doi.org/10.1137/23m1555223","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2041-2068, September 2024. <br/> Abstract. This paper describes several cases of adjunction in the homomorphism preorder of relational structures. We say that two functors [math] and [math] between thin categories of relational structures are adjoint if for all structures [math] and [math], we have that [math] maps homomorphically to [math] if and only if [math] maps homomorphically to [math]. If this is the case, [math] is called the left adjoint to [math] and [math] the right adjoint to [math]. Foniok and Tardif [Discrete Math., 338 (2015), pp. 527–535] described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr [Reports of the Midwest Category Seminar IV, Lecture Notes in Math. 137, Springer, 1970, pp. 100–113]. We generalize results of Foniok and Tardif to arbitrary relational structures, and coincidently, we also provide more right adjoints on digraphs, and since these constructions are connected to finite duality, we also provide a new construction of duals to trees. Our results are inspired by an application in promise constraint satisfaction—it has been shown that such functors can be used as efficient reductions between these problems.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Partial Reflections and Globally Linked Pairs in Rigid Graphs 刚性图中的局部反射和全局关联对

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-03 DOI: 10.1137/23m157065x

Dániel Garamvölgyi, Tibor Jordán

{"title":"Partial Reflections and Globally Linked Pairs in Rigid Graphs","authors":"Dániel Garamvölgyi, Tibor Jordán","doi":"10.1137/23m157065x","DOIUrl":"https://doi.org/10.1137/23m157065x","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2005-2040, September 2024. <br/> Abstract. A [math]-dimensional framework is a pair [math], where [math] is a graph and [math] maps the vertices of [math] to points in [math]. The edges of [math] are mapped to the corresponding line segments. A graph [math] is said to be globally rigid in [math] if every generic [math]-dimensional framework [math] is determined, up to congruence, by its edge lengths. A finer property is global linkedness: we say that a vertex pair [math] of [math] is globally linked in [math] in [math] if in every generic [math]-dimensional framework [math] the distance between [math] and [math] is uniquely determined by the edge lengths. In this paper we investigate globally linked pairs in graphs in [math]. We give several characterizations of those rigid graphs [math] in which a pair [math] is globally linked if and only if there exist [math] internally disjoint paths from [math] to [math] in [math]. We call these graphs [math]-joined. Among others, we show that [math] is [math]-joined if and only if for each pair of generic frameworks of [math] with the same edge lengths, one can be obtained from the other by a sequence of partial reflections along hyperplanes determined by [math]-separators of [math]. We also show that the family of [math]-joined graphs is closed under edge addition, as well as under gluing along [math] or more vertices. As a key ingredient to our main results, we prove that rigid graphs in [math] contain no crossing [math]-separators. Our results give rise to new families of graphs for which global linkedness (and global rigidity) in [math] can be tested in polynomial time.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Erratum: Multitasking Capacity: Hardness Results and Improved Constructions 勘误：多任务处理能力：硬度结果和改进结构

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-26 DOI: 10.1137/23m1603856

Noga Alon, Jonathan D. Cohen, Thomas L. Griffiths, Pasin Manurangsi, Daniel Reichman, Igor Shinkar, Tal Wagner

引用次数: 0

Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs 高维几何非均质随机图中的群集

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-25 DOI: 10.1137/23m157394x

Tobias Friedrich, Andreas Göbel, Maximilian Katzmann, Leon Schiller

{"title":"Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs","authors":"Tobias Friedrich, Andreas Göbel, Maximilian Katzmann, Leon Schiller","doi":"10.1137/23m157394x","DOIUrl":"https://doi.org/10.1137/23m157394x","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1943-2000, June 2024. <br/> Abstract. A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach nongeometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Tropical Critical Points of an Affine Matroid 仿射矩阵的热带临界点

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-24 DOI: 10.1137/23m1556174

Federico Ardila-Mantilla, Christopher Eur, Raul Penaguiao

引用次数: 0

On the Weisfeiler–Leman Dimension of Permutation Graphs 关于置换图的 Weisfeiler-Leman 维度

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-21 DOI: 10.1137/23m1575019

Jin Guo, Alexander L. Gavrilyuk, Ilia Ponomarenko

引用次数: 0

Phase Transitions of Structured Codes of Graphs 图的结构化编码的相变

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-19 DOI: 10.1137/23m1614572

Bo Bai, Yu Gao, Jie Ma, Yuze Wu

引用次数: 0

On Graphs Coverable by [math] Shortest Paths 论[数学]最短路径可覆盖的图

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-10 DOI: 10.1137/23m1564511

Maël Dumas, Florent Foucaud, Anthony Perez, Ioan Todinca

引用次数: 0