ACM Transactions on Algorithms (TALG)最新文献_第2页

Max Flows in Planar Graphs with Vertex Capacities 具有顶点容量的平面图形中的最大流

ACM Transactions on Algorithms (TALG) Pub Date : 2022-01-22 DOI: 10.1145/3504032

Yipu Wang

{"title":"Max Flows in Planar Graphs with Vertex Capacities","authors":"Yipu Wang","doi":"10.1145/3504032","DOIUrl":"https://doi.org/10.1145/3504032","url":null,"abstract":"We consider the maximum flow problem in directed planar graphs with capacities on both vertices and arcs and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in O(min {k2 n, n log3 n + kn}) time when all capacities are bounded by a constant, where n is the number of vertices in the graph, and k is the number of terminals. This algorithm is the first to solve the vertex-disjoint paths problem in linear time when k is fixed but larger than 2. The second algorithm runs in O(k5 Δ n polylog (nU)) time, where each arc capacity and finite vertex capacity is bounded by U, and Δ is the maximum degree of the graph. Finally, when k = 3, we present an algorithm that runs in O(n log n) time; this algorithm works even when the capacities are arbitrary reals. Our algorithms improve on the fastest previously known algorithms when k and Δ are fixed and U is bounded by a polynomial in n. Prior to this result, the fastest algorithms ran in O(n4/3+o(1)) time for unit capacities; in the smallest of O(n3/2log n log U), Õ(n10/7U1/7), O(n11/8+o(1)U1/4), and O(n4/3 + o(1)U1/3) time for integer capacities; and in O(n2/log n) time for real capacities, even when k = 3.","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122347537","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

The Quest for Strong Inapproximability Results with Perfect Completeness 对具有完全完备性的强不近似结果的追求

ACM Transactions on Algorithms (TALG) Pub Date : 2021-07-12 DOI: 10.1145/3459668

Joshua Brakensiek, V. Guruswami

{"title":"The Quest for Strong Inapproximability Results with Perfect Completeness","authors":"Joshua Brakensiek, V. Guruswami","doi":"10.1145/3459668","DOIUrl":"https://doi.org/10.1145/3459668","url":null,"abstract":"The Unique Games Conjecture has pinned down the approximability of all constraint satisfaction problems (CSPs), showing that a natural semidefinite programming relaxation offers the optimal worst-case approximation ratio for any CSP. This elegant picture, however, does not apply for CSP instances that are perfectly satisfiable, due to the imperfect completeness inherent in the Unique Games Conjecture. This work is motivated by the pursuit of a better understanding of the approximability of perfectly satisfiable instances of CSPs. We prove that an “almost Unique” version of Label Cover can be approximated within a constant factor on satisfiable instances. Our main conceptual contribution is the formulation of a (hypergraph) version of Label Cover that we call V Label Cover. Assuming a conjecture concerning the inapproximability of V Label Cover on perfectly satisfiable instances, we prove the following implications: • There is an absolute constant c0 such that for k ≥ 3, given a satisfiable instance of Boolean k-CSP, it is hard to find an assignment satisfying more than c0k2/2k fraction of the constraints. • Given a k-uniform hypergraph, k ≥ 2, for all ε > 0, it is hard to tell if it is q-strongly colorable or has no independent set with an ε fraction of vertices, where q=⌈k+√k-1/2⌉. • Given a k-uniform hypergraph, k ≥ 3, for all ε > 0, it is hard to tell if it is (k-1)-rainbow colorable or has no independent set with an ε fraction of vertices.","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123608653","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: 16

Online Service with Delay 网上服务有延误

ACM Transactions on Algorithms (TALG) Pub Date : 2021-07-12 DOI: 10.1145/3459925

Y. Azar, Arun Ganesh, Rong Ge, Debmalya Panigrahi

引用次数: 1

Discrete Fréchet Distance under Translation 翻译下的离散距离

ACM Transactions on Algorithms (TALG) Pub Date : 2021-07-12 DOI: 10.1145/3460656

K. Bringmann, Marvin Künnemann, A. Nusser

{"title":"Discrete Fréchet Distance under Translation","authors":"K. Bringmann, Marvin Künnemann, A. Nusser","doi":"10.1145/3460656","DOIUrl":"https://doi.org/10.1145/3460656","url":null,"abstract":"The discrete Fréchet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fréchet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length n in the plane, the fastest known algorithm runs in time Õ(n5) [12]. This is achieved by constructing an arrangement of disks of size Õ(n4), and then traversing its faces while updating reachability in a directed grid graph of size N := Õ(n5), which can be done in time Õ(√ N) per update [27]. The contribution of this article is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than Õ(√ N), we improve this part of the algorithm: We observe that an offline variant of dynamic s-t-reachability in directed grid graphs suffices, and we solve this variant in amortized time Õ(N1/3) per update, resulting in an improved running time of Õ(N4.66) for the discrete Fréchet distance under translation. Second, we provide evidence that constructing the arrangement of size Õ(N4) is necessary in the worst case by proving a conditional lower bound of n4 - o(1) on the running time for the discrete Fréchet distance under translation, assuming the Strong Exponential Time Hypothesis.","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126711371","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: 3

Approximate Counting of k-Paths: Simpler, Deterministic, and in Polynomial Space k-路径的近似计数:更简单的，确定性的，在多项式空间

ACM Transactions on Algorithms (TALG) Pub Date : 2021-07-12 DOI: 10.1145/3461477

D. Lokshtanov, Andreas Björklund, Saket Saurabh, M. Zehavi

引用次数: 5

On β-Plurality Points in Spatial Voting Games 论空间投票游戏中的β-复数点

ACM Transactions on Algorithms (TALG) Pub Date : 2021-07-12 DOI: 10.1145/3459097

B. Aronov, M. D. Berg, Joachim Gudmundsson, M. Horton

{"title":"On β-Plurality Points in Spatial Voting Games","authors":"B. Aronov, M. D. Berg, Joachim Gudmundsson, M. Horton","doi":"10.1145/3459097","DOIUrl":"https://doi.org/10.1145/3459097","url":null,"abstract":"Let V be a set of n points in mathcal Rd, called voters. A point p ∈ mathcal Rd is a plurality point for V when the following holds: For every q ∈ mathcal Rd, the number of voters closer to p than to q is at least the number of voters closer to q than to p. Thus, in a vote where each v∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal p will not lose against any alternative proposal q. For most voter sets, a plurality point does not exist. We therefore introduce the concept of β-plurality points, which are defined similarly to regular plurality points, except that the distance of each voter to p (but not to q) is scaled by a factor β, for some constant 0< β ⩽ 1. We investigate the existence and computation of β-plurality points and obtain the following results. • Define β*d := {β : any finite multiset V in mathcal Rd admits a β-plurality point. We prove that β*d = √3/2, and that 1/√ d ⩽ β*d ⩽ √ 3/2 for all d⩾ 3. • Define β (p, V) := sup {β : p is a β -plurality point for V}. Given a voter set V in mathcal R2, we provide an algorithm that runs in O(n log n) time and computes a point p such that β (p, V) ⩾ β*b. Moreover, for d⩾ 2, we can compute a point p with β (p,V) ⩾ 1/√ d in O(n) time. • Define β (V) := sup { β : V admits a β -plurality point}. We present an algorithm that, given a voter set V in mathcal Rd, computes an ((1-ɛ)ċ β (V))-plurality point in time On2ɛ 3d-2 ċ log n ɛ d-1 ċ log 2 1ɛ).","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129472682","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: 2

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space 低空间非随机化大规模并行计算的图稀疏化

ACM Transactions on Algorithms (TALG) Pub Date : 2021-05-29 DOI: 10.1145/3451992

A. Czumaj, Peter Davies, M. Parter

{"title":"Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space","authors":"A. Czumaj, Peter Davies, M. Parter","doi":"10.1145/3451992","DOIUrl":"https://doi.org/10.1145/3451992","url":null,"abstract":"The Massively Parallel Computation (MPC) model is an emerging model that distills core aspects of distributed and parallel computation, developed as a tool to solve combinatorial (typically graph) problems in systems of many machines with limited space. Recent work has focused on the regime in which machines have sublinear (in n, the number of nodes in the input graph) space, with randomized algorithms presented for the fundamental problems of Maximal Matching and Maximal Independent Set. However, there have been no prior corresponding deterministic algorithms. A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all edges incident to a single node. This poses a considerable obstacle compared to classical models in which each node is assumed to know and have easy access to its incident edges. To overcome this barrier, we introduce a new graph sparsification technique that deterministically computes a low-degree subgraph, with the additional property that solving the problem on this subgraph provides significant progress towards solving the problem for the original input graph. Using this framework to derandomize the well-known algorithm of Luby [SICOMP’86], we obtain O(log Δ + log log n)-round deterministic MPC algorithms for solving the problems of Maximal Matching and Maximal Independent Set with O(nɛ) space on each machine for any constant ɛ > 0. These algorithms also run in O(log Δ) rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of O(log 2Δ) rounds by Censor-Hillel et al. [DISC’17].","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121678517","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

Sparse Backbone and Optimal Distributed SINR Algorithms 稀疏主干与最优分布SINR算法

ACM Transactions on Algorithms (TALG) Pub Date : 2021-05-29 DOI: 10.1145/3452937

M. Halldórsson, Tigran Tonoyan

引用次数: 3

Navigating in Trees with Permanently Noisy Advice 导航树与永久嘈杂的建议

ACM Transactions on Algorithms (TALG) Pub Date : 2021-05-29 DOI: 10.1145/3448305

Lucas Boczkowski, U. Feige, Amos Korman, Yoav Rodeh

{"title":"Navigating in Trees with Permanently Noisy Advice","authors":"Lucas Boczkowski, U. Feige, Amos Korman, Yoav Rodeh","doi":"10.1145/3448305","DOIUrl":"https://doi.org/10.1145/3448305","url":null,"abstract":"We consider a search problem on trees in which an agent starts at the root of a tree and aims to locate an adversarially placed treasure, by moving along the edges, while relying on local, partial information. Specifically, each node in the tree holds a pointer to one of its neighbors, termed advice. A node is faulty with probability q. The advice at a non-faulty node points to the neighbor that is closer to the treasure, and the advice at a faulty node points to a uniformly random neighbor. Crucially, the advice is permanent, in the sense that querying the same node again would yield the same answer. Let Δ denote the maximum degree. For the expected number of moves (edge traversals) until finding the treasure, we show that a phase transition occurs when the noise parameter q is roughly 1 √Δ. Below the threshold, there exists an algorithm with expected number of moves O(D √Δ), where D is the depth of the treasure, whereas above the threshold, every search algorithm has an expected number of moves, which is both exponential in D and polynomial in the number of nodes n. In contrast, if we require to find the treasure with probability at least 1 − δ, then for every fixed ɛ > 0, if q < 1/Δɛ, then there exists a search strategy that with probability 1 − δ finds the treasure using (Δ −1D)O(1/ε) moves. Moreover, we show that (Δ −1D)Ω(1/ε) moves are necessary.","PeriodicalId":154047,"journal":{"name":"ACM Transactions on Algorithms (TALG)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121466951","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

A Simple Algorithm for Optimal Search Trees with Two-way Comparisons 具有双向比较的最优搜索树的简单算法

ACM Transactions on Algorithms (TALG) Pub Date : 2021-03-01 DOI: 10.1145/3477910

M. Chrobak, M. Golin, J. Munro, N. Young

引用次数: 6