SIAM Journal on Computing最新文献_第9页

Special Section on the Fifty-First Annual ACM Sympositum on the Theory of Computing (STOC 2019) 第五十一届ACM计算理论年会(STOC 2019)专题讨论

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-27 DOI: 10.1137/23n975661

Dana Moshkovitz, Sushant Sachdeva

引用次数: 0

Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg–Rao 全动态电流:稀疏Maxflow比Goldberg-Rao更快

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-26 DOI: 10.1137/22m1476666

Yu Gao, Yang Liu, Richard Peng

引用次数: 0

Approximately Counting Independent Sets of a Given Size in Bounded-Degree Graphs 有界度图中给定大小的独立集的近似计数

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-26 DOI: 10.1137/21m1466220

Ewan Davies, Will Perkins

引用次数: 0

An Optimal Separation of Randomized and Quantum Query Complexity 随机查询复杂度与量子查询复杂度的最优分离

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-26 DOI: 10.1137/22m1468943

Alexander A. Sherstov, Andrey A. Storozhenko, Pei Wu

{"title":"An Optimal Separation of Randomized and Quantum Query Complexity","authors":"Alexander A. Sherstov, Andrey A. Storozhenko, Pei Wu","doi":"10.1137/22m1468943","DOIUrl":"https://doi.org/10.1137/22m1468943","url":null,"abstract":"We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order sum to at most , where is the number of variables, is the tree depth, and is an absolute constant. This bound is essentially tight and settles a conjecture due to Tal [Towards optimal separations between quantum and randomized query complexities, in Proceedings of the Sixty-First Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2020, pp. 228–239]. The bounds prior to our work degraded rapidly with , becoming trivial already at . As an application, we obtain, for every integer , a partial Boolean function on bits that has bounded-error quantum query complexity at most and randomized query complexity . This separation of bounded-error quantum versus randomized query complexity is best possible, by the results of Aaronson and Ambainis [SIAM J. Comput., 47 (2018), pp. 982–1038] and Bravyi et al. [Classical Algorithms for Forrelation, arXiv preprint, 2021]. Prior to our work, the best known separation was polynomially weaker: versus for any [A. Tal, Towards optimal separations between quantum and randomized query complexities, in Proceedings of the Sixty-First Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2020, pp. 228–239]. As another application, we obtain an essentially optimal separation of versus for bounded-error quantum versus randomized communication complexity for any . The best previous separation was polynomially weaker: versus (this is implicit in [A. Tal, Towards optimal separations between quantum and randomized query complexities, in Proceedings of the Sixty-First Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2020, pp. 228–239]).","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136267126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness 张量、群和多项式的同构问题的复杂性I:张量同构-完备性

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-26 DOI: 10.1137/21m1441110

Joshua Grochow, Youming Qiao

引用次数: 0

Bridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger Approaches 弥合树和连接性增强之间的差距:统一和更强大的方法

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-12 DOI: 10.1137/21m1430601

Federica Cecchetto, Vera Traub, Rico Zenklusen

{"title":"Bridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger Approaches","authors":"Federica Cecchetto, Vera Traub, Rico Zenklusen","doi":"10.1137/21m1430601","DOIUrl":"https://doi.org/10.1137/21m1430601","url":null,"abstract":"We consider the connectivity augmentation problem (CAP), a classical problem in the area of survivable network design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a -edge-connected graph and a set of extra edges, the task is to find a minimum cardinality subset of extra edges whose addition to makes the graph -edge-connected. If is odd, the problem is known to reduce to the tree augmentation problem (TAP)—i.e., is a spanning tree—for which significant progress has been achieved recently, leading to approximation factors below 1.5 (the current best factor is 1.458). However, advances on TAP have not carried over to CAP so far. Indeed, only very recently, Byrka, Grandoni, and Ameli [Proceedings of the 52nd ACM Symposium on Theory of Computing, 2020, pp. 815–825] managed to obtain the first approximation factor below 2 for CAP by presenting a 1.91-approximation algorithm based on a method that is disjoint from recent advances for TAP. We first bridge the gap between TAP and CAP by presenting techniques that allow for leveraging insights and methods from TAP to approach CAP. We then introduce a new way to get approximation factors below 1.5, based on a new analysis technique. Through these ingredients, we obtain a 1.393-approximation algorithm for CAP, and therefore also for TAP. This leads to the current best approximation result for both problems in a unified way, by significantly improving on the abovementioned 1.91-approximation for CAP and also the previously best approximation factor of 1.458 for TAP by Grandoni, Kalaitzis, and Zenklusen [Proceedings of the 50th ACM Symposium on Theory of Computing, 2018, pp. 632–645]. Additionally, a feature we inherit from recent TAP advances is that our approach can deal with the weighted setting when the ratio of the largest to smallest cost on extra links is bounded, in which case we obtain approximation factors below 1.5.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135289251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Consensus-Halving: Does It Ever Get Easier? 共识减半:它会变得更容易吗?

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-04 DOI: 10.1137/20m1387493

Aris Filos-Ratsikas, Alexandros Hollender, Katerina Sotiraki, Manolis Zampetakis

{"title":"Consensus-Halving: Does It Ever Get Easier?","authors":"Aris Filos-Ratsikas, Alexandros Hollender, Katerina Sotiraki, Manolis Zampetakis","doi":"10.1137/20m1387493","DOIUrl":"https://doi.org/10.1137/20m1387493","url":null,"abstract":"In the $varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label \"$+$\" or \"$-$\" to each piece, such that every agent values the total amount of \"$+$\" and the total amount of \"$-$\" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first \"natural\" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $varepsilon$-Consensus-Halving for any $varepsilon$, as well as a polynomial-time algorithm for $varepsilon=1/2$. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem [Simmons and Su, 2003]. In particular, we prove that $varepsilon$-Consensus-$1/3$-Division is PPAD-hard.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136049107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Spectral Methods from Tensor Networks 张量网络的谱方法

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-04-04 DOI: 10.1137/20m1311661

Ankur Moitra, Alexander S. Wein

引用次数: 1

Want to Gather? No Need to Chatter! 想要聚会吗?没有必要喋喋不休!

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-03-15 DOI: 10.1137/20m1362899

Sébastien Bouchard, Yoann Dieudonné, Andrzej Pelc

{"title":"Want to Gather? No Need to Chatter!","authors":"Sébastien Bouchard, Yoann Dieudonné, Andrzej Pelc","doi":"10.1137/20m1362899","DOIUrl":"https://doi.org/10.1137/20m1362899","url":null,"abstract":"A team of mobile agents with different labels, starting from different nodes of an unknown anonymous network, must meet at the same node and declare that they all met. This task of gathering was traditionally considered assuming that agents at the same node can exchange information. We ask if this ability of talking is needed. The answer turns out to be no. We design two deterministic algorithms that accomplish gathering in a much weaker model. We only assume that each agent knows how many agents are at the node that it currently occupies. Our first algorithm assumes that agents know some upper bound N on the size of the network, and works in time polynomial in N and in the length of the smallest label. Our second algorithm does not assume any knowledge about the network, but its complexity is at least exponential in the size of the network and in the labels of agents. Its purpose is to show feasibility of gathering under this harsher scenario. As a by-product we solve, in the same weak model, the fundamental problem of leader election among agents. As an application we solve the gossiping problem in this model: if each agent has a message, all agents can learn all messages. This is perhaps our most surprising finding: agents without any transmitting devices can solve the most general information exchange problem if they can count the number of agents present at visited nodes.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135598817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Isomorphism Testing for Graphs Excluding Small Minors 不包含小次的图的同构检验

3区计算机科学

SIAM Journal on Computing Pub Date : 2023-02-28 DOI: 10.1137/21m1401930

Martin Grohe, Daniel Neuen, Daniel Wiebking

引用次数: 0