Theoretical Computer Science最新文献_第2页

The monadic theory of toric words 环状词的一元论

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-14 DOI: 10.1016/j.tcs.2024.114959

Valérie Berthé , Toghrul Karimov , Joris Nieuwveld , Joël Ouaknine , Mihir Vahanwala , James Worrell

For which unary predicates

P_{1}, \dots, P_{m}

is the MSO theory of the structure

〈 N; <, P_{1}, \dots, P_{m} 〉

decidable? We survey the state of the art, leading us to investigate combinatorial properties of almost-periodic, morphic, and toric words. In doing so, we show that if each

P_{i}

can be generated by a toric dynamical system of a certain kind, then the attendant MSO theory is decidable. We give various applications of toric words, including the recent result of [1] that the MSO theory of

〈 N; <, {2^{n} : n \in N}, {3^{n} : n \in N} 〉

is decidable.

对于哪些一元谓词 P1、......、Pm，〈N;<,P1,......,Pm〉结构的 MSO 理论是可解的？我们考察了这一领域的现状，并由此研究了近周期词、形态词和环状词的组合性质。在此过程中，我们证明，如果每个 Pi 都可以由某类环状动力系统生成，那么相应的 MSO 理论就是可解的。我们给出了环状词的各种应用，包括 [1] 的最新结果：〈N;<,{2n:n∈N},{3n:n∈N}〉的 MSO 理论是可判定的。

引用次数: 0

On MAX–SAT with cardinality constraint 关于具有卡片数量限制的 MAX-SAT

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-14 DOI: 10.1016/j.tcs.2024.114971

Fahad Panolan , Hannane Yaghoubizade

We consider the weighted MAX–SAT problem with an additional constraint that at most k variables can be set to true. We call this problem k–WMAX–SAT. This problem admits a

(1 - \frac{1}{e})

-factor approximation algorithm in polynomial time [Sviridenko, Algorithmica (2001)] and it is proved that there is no

(1 - \frac{1}{e} + ϵ)

-factor approximation algorithm in

f (k) \cdot n^{o (k)}

time for Maximum Coverage, the unweighted monotone version of k–WMAX–SAT [Manurangsi, SODA 2020]. Therefore, we study two restricted versions of the problem in the realm of parameterized complexity.

1.
When the input is an unweighted 2–CNF formula (the problem is called k–MAX–2SAT), we design an efficient polynomial-size approximate kernelization scheme. That is, we design a polynomial-time algorithm that given a 2–CNF formula ψ and $ϵ > 0$ , compresses the input instance to a 2–CNF formula $ψ^{⋆}$ such that any c-approximate solution of $ψ^{⋆}$ can be converted to a $c (1 - ϵ)$ -approximate solution of ψ in polynomial time.
2.
When the input is a planar CNF formula, i.e., the variable-clause incidence graph is a planar graph, we show the following results:
- •
  There is an FPT algorithm for k–WMAX–SAT on planar CNF formulas that runs in $2^{O (k)} \cdot (C + V)$ time.
- •
  There is a polynomial-time approximation scheme for k–WMAX–SAT on planar CNF formulas that runs in time $2^{O (\frac{1}{ϵ})} \cdot k \cdot (C + V)$ .
The above-mentioned C and V are the number of clauses and variables of the input formula respectively.

我们考虑的是加权 MAX-SAT 问题，它有一个额外的约束条件，即最多有 k 个变量可以设为 true。我们称这个问题为 k-WMAX-SAT。这个问题允许在多项式时间内使用 (1-1e)- 因子近似算法[Sviridenko, Algorithmica (2001)]，并且证明对于最大覆盖率（k-WMAX-SAT 的非加权单调版本），在 f(k)⋅no(k) 时间内没有 (1-1e+ϵ)- 因子近似算法[Manurangsi, SODA 2020]。因此，我们在参数化复杂度领域研究了该问题的两个限制版本。1.当输入是一个无权 2-CNF 公式时（该问题称为 k-MAX-2SAT），我们设计了一个高效的多项式大小近似内核化方案。也就是说，我们设计了一种多项式时间算法，在给定 2-CNF 公式 ψ 和 ϵ>0 的情况下，将输入实例压缩为 2-CNF 公式 ψ⋆，使得 ψ⋆的任何 c 近似解都能在多项式时间内转换为 ψ 的 c(1-ϵ)- 近似解。当输入为平面 CNF 公式时，即2 .当输入为平面 CNF 公式时，即变量句入射图为平面图时，我们展示了以下结果：-存在一种平面 CNF 公式 k-WMAX-SAT 的 FPT 算法，其运行时间为 2O(k)⋅(C+V)；-存在一种平面 CNF 公式 k-WMAX-SAT 的多项式时间近似方案，其运行时间为 2O(1ϵ)⋅k⋅(C+V)。上述 C 和 V 分别是输入公式的分句数和变量数。

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引用次数: 0

Approximating the shortest path problem with scenarios 用场景近似最短路径问题

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-13 DOI: 10.1016/j.tcs.2024.114972

Adam Kasperski, Paweł Zieliński

This paper discusses the shortest path problem in a general directed graph with n nodes and K cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to approximate within

Ω (\log^{1 - ϵ} K)

for any

ϵ > 0

unless NP

\subseteq DTIME (n^{polylog n})

even for arc series-parallel graphs and within

Ω (\log n / \log \log n)

unless NP

\subseteq ZPTIME (n^{\log \log n})

for acyclic graphs. The best approximation algorithm for the min-max shortest path problem in general graphs, known to date, has an approximation ratio of K. In this paper, an

\tilde{O} (\sqrt{n})

flow LP-based approximation algorithm for min-max shortest path in general graphs is constructed. It is also shown that the approximation ratio obtained is close to an integrality gap of the corresponding flow LP relaxation.

本文讨论的是一般有向图中的最短路径问题，该图有 n 个节点和 K 个成本方案（目标）。为了选择一个解，采用了最小-最大准则。对于任意ϵ>0，除非 NP ⊆DTIME(npolylogn)，否则即使对于弧序列平行图，最小-最大版本的问题也很难在Ω(log1-ϵK)内逼近；对于非循环图，除非 NP ⊆ZPTIME(nloglogn)，否则也很难在Ω(logn/loglogn)内逼近。本文构建了基于 O˜(n)流 LP 的一般图中最小最短路径的近似算法。研究还表明，所获得的近似率接近于相应流 LP 松弛的积分差距。

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引用次数: 0

Retraction notice to “Optimizing Scalability and Availability of Cloud Based Software Services Using Modified Scale Rate Limiting Algorithm” [Theoretical computer science 943 (2023) 230-240] 基于云的软件服务的可扩展性和可用性优化（使用修改后的规模速率限制算法）"的撤稿通知 [Theoretical computer science 943 (2023) 230-240]

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-09 DOI: 10.1016/j.tcs.2024.114944

V.L. Padma Latha , N. Sudhakar Reddy , A. Suresh Babu

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/locate/withdrawalpolicy).

This article has been retracted at the request of the Editor-in-Chief of Theoretical Computer Science, Section A.

The article is a duplicate of a paper that has already been published in Int. J. Nonlinear Anal. Appl., Volume 13 (2022), Issue 2, Pages 1893-1905, http://dx.doi.org/10.22075/ijnaa.2022.27403.3588. One of the conditions of submission of a paper for publication is therefore that authors declare explicitly that the paper has not been previously published and is not under consideration for publication elsewhere. As such this article represents a misuse of the scientific publishing system.

The scientific community takes a very strong view on this matter and apologies are offered to readers of the journal that this was not detected during the submission process.

这篇文章已被撤回：请参阅 Elsevier Policy on Article Withdrawal (https://www.elsevier.com/locate/withdrawalpolicy)。应《理论计算机科学》A 部分主编的要求，这篇文章已被撤回。该文章与已发表在 Int.J. Nonlinear Anal.Appl.，第 13 卷（2022 年），第 2 期，第 1893-1905 页，http://dx.doi.org/10.22075/ijnaa.2022.27403.3588。因此，提交论文发表的条件之一是作者明确声明该论文之前未曾发表，也未考虑在其他地方发表。因此，这篇文章是对科学出版系统的滥用。科学界对此事的看法非常强烈，在投稿过程中没有发现这一点，特此向本刊读者致歉。

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引用次数: 0

Geography, Kotzig's Nim, and variants 地理、科茨希的尼姆和变体

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-06 DOI: 10.1016/j.tcs.2024.114957

Srinivas Arun

Geography is a combinatorial game in which two players take turns moving a token along edges of a directed graph and deleting the vertex they came from. We expand upon work by Fox and Geissler, who classified the computational complexity of determining the winner of various Geography variants given a graph. In particular, we show NP-hardness for undirected partizan Geography with free deletion on bipartite graphs and directed partizan Geography with free deletion on acyclic graphs. In addition, we study Kotzig's Nim, a special case of Geography where the vertices are labeled and moves correspond to additions by fixed amounts. We partially resolve a conjecture by Tan and Ward about games with a certain move set.

地理学是一种组合游戏，在游戏中，两名玩家轮流沿着有向图的边移动一个标记，并删除它们所来自的顶点。福克斯和盖斯勒对给定图的各种地理变体中确定胜者的计算复杂度进行了分类，我们在此基础上对他们的工作进行了扩展。特别是，我们证明了在双向图上自由删除的无向偏态地理学和在无环图上自由删除的有向偏态地理学的 NP-hardness。此外，我们还研究了 Kotzig's Nim，这是地理学的一种特例，其中顶点是有标签的，移动对应于固定数量的添加。我们部分地解决了 Tan 和 Ward 关于具有特定移动集的博弈的猜想。

引用次数: 0

Distributed computing in the asynchronous LOCAL model 异步 LOCAL 模式中的分布式计算

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-05 DOI: 10.1016/j.tcs.2024.114952

Carole Delporte-Gallet, Hugues Fauconnier, Pierre Fraigniaud, Mikaël Rabie

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any task T associated to a locally checkable labeling (lcl), if T is solvable in t rounds by a deterministic algorithm in the LOCAL model, then T remains solvable by a deterministic algorithm in

O (t)

rounds in an asynchronous variant of the LOCAL model whenever

t = O (polylog n)

. This improves the result by Castañeda et al. [TCS, 2019], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the LOCAL model, as long as the communications remain synchronous and failure-free. To this end, this paper introduces a new distributed renaming technique to provide nodes with consistent identifiers.

LOCAL 模型是在分布式网络计算框架内研究局部性的主要模型之一。不过，该模型也受到一些相关批评，包括所有节点同时唤醒、以锁定步骤执行、无故障等事实。我们证明，在一定程度上放宽这些假设并不会损害本地计算。特别是，我们证明，对于与本地可检查标记（lcl）相关的任何任务 T，如果在 LOCAL 模型中，T 可通过确定性算法在 t 轮内求解，那么在 LOCAL 模型的异步变体中，只要 t=O(polylogn)，T 仍可通过确定性算法在 O(t) 轮内求解。这改进了卡斯塔涅达等人[TCS, 2019]的结果，后者仅限于对环进行 3 着色。更广义地说，本文的主要贡献在于证明，只要通信保持同步和无故障，计算中的异步和故障并不会限制 LOCAL 模型的威力，这一点也许令人惊讶。为此，本文引入了一种新的分布式重命名技术，为节点提供一致的标识符。

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引用次数: 0

Structural parameterizations of vertex integrity 顶点完整性的结构参数化

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-11-04 DOI: 10.1016/j.tcs.2024.114954

Tatsuya Gima , Tesshu Hanaka , Yasuaki Kobayashi , Ryota Murai , Hirotaka Ono , Yota Otachi

The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts. We also show that the vertex integrity can be approximated within an

O (\log opt)

factor.

图参数顶点完整性衡量的是一个图在删除少量顶点时的脆弱程度。更确切地说，具有小顶点完整性的图允许删除少量顶点，以使剩余的连通成分变小。在本文中，我们开始系统地研究计算无权/有权顶点完整性问题的结构参数化。作为结构图参数，我们考虑了众所周知的参数，如 clique-width、treewidth、pathwidth、treedepth、modular-width、邻域多样性、孪生覆盖数和簇顶点删除数。我们展示了几个正反结果，并提出了鲜明的复杂性对比。我们还表明，顶点完整性可在 O(logopt) 因子范围内近似。

引用次数: 0

Instance-optimal information-based voting 基于信息的实例最优投票

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-31 DOI: 10.1016/j.tcs.2024.114945

Flavio Chierichetti

<div><div>The classical Condorcet Jury Theorem considers a voting scenario in which there exists a candidate whose election would be ideal for each voter; each voter, though, has only a limited understanding of the world and is thus unable to determine exactly who this candidate is. The main question in this scenario is whether the voters, acting individually, can cast their ballots so that the unknown optimal candidate wins the election, and the welfare of the group of voters is maximized.</div><div>In this setting, each candidate is represented by a known probability distribution over signals about the world that the voters can perceive, that is, over bits. One of these candidates is chosen (secretively, by an adversary) to be the <em>ideal</em> candidate. Afterwards, each voter samples this unknown candidate's distribution once and casts a ballot with the hope that the unknown ideal candidate wins the election.</div><div>In this paper, we consider the famous Condorcet voting system, as well as some of its variants. First, we give a positive answer to an open question of Chierichetti and Kleinberg <span><span>[8]</span></span>, and show that, with Condorcet voting, there exists a uniform voting strategy that makes the group of voters succeed with probability <span><math><mn>1</mn><mo>−</mo><mi>δ</mi></math></span> provided that <span><math><mi>Θ</mi><mrow><mo>(</mo><msubsup><mrow><mi>ϵ</mi></mrow><mrow><mi>tv</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msubsup><mo>⋅</mo><mi>ln</mi><mo>⁡</mo><msup><mrow><mi>δ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> voters take part in the election — here, <span><math><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>tv</mi></mrow></msub></math></span> is the minimum total variation distance between the distributions of two candidates.</div><div>We also give a uniform voting strategy for the Copeland voting system (a variant of Condorcet) that makes the group succeed with probability <span><math><mn>1</mn><mo>−</mo><mi>δ</mi></math></span> with <span><math><mi>Θ</mi><mrow><mo>(</mo><msubsup><mrow><mi>ϵ</mi></mrow><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msubsup><mo>⋅</mo><mi>ln</mi><mo>⁡</mo><msup><mrow><mi>δ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> voters, where <span><math><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> is the minimum Hellinger distance between the distributions. Our uniform Copeland strategy, then, is an <em>instance-optimal</em> hypothesis testing algorithm: constants aside, the strategy is as efficient as the optimal omniscient algorithm which determines the unknown candidate after having directly observed each of the signals perceived by the voters. Then, we “derandomize” our uniform Copeland strategy, and obtain a Condorcet strategy that achieves instance-optimality at the cost of losing uniformity; finally, we prove that this loss of uniformity is necessary: no uniform Co

经典的孔多塞陪审员定理考虑了这样一种投票情况：存在一个候选人，其当选对每个选民来说都是最理想的；但每个选民对世界的了解都很有限，因此无法确定这个候选人到底是谁。在这种情况下，每个候选人都由一个已知的概率分布来表示，这个概率分布是关于选民所能感知到的世界的信号，也就是关于比特的信号。在这些候选者中，（由对手秘密地）选择一个作为理想候选者。之后，每个投票人都会对这个未知候选人的分布进行一次采样，并投出一张选票，希望这个未知的理想候选人赢得选举。在本文中，我们将考虑著名的康德赛特投票系统及其一些变体。首先，我们给出了奇里切蒂和克莱因伯格[8]的一个开放问题的正面答案，并证明在孔多塞投票制下，只要有Θ(ϵtv-2⋅lnδ-1)个选民参加选举，就存在一种均匀投票策略，它能使选民组以 1-δ 的概率成功--这里，ϵtv 是两个候选人分布之间的最小总变异距离。我们还给出了科普兰投票系统（康德赛特的一种变体）的统一投票策略，该策略能使Θ(ϵH-2⋅lnδ-1) 选民组成的小组以 1-δ 的概率成功，其中ϵH 是两个分布之间的最小海灵格距离。因此，我们的统一谷轮策略是一种实例最优的假设检验算法：撇开常数不谈，该策略与最优的全知算法一样高效，后者在直接观察到选民感知到的每个信号后，确定未知的候选人。然后，我们将统一的科普兰策略 "去随机化"，得到了一种康德赛特策略，它以失去统一性为代价实现了实例最优；最后，我们证明这种统一性的损失是必要的：一般来说，没有一种统一的康德赛特策略能实现实例最优。因此，正确的投票策略能让这些经典的组合投票系统达到与集中式最优假设检验器相同的效率。

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引用次数: 0

Parking problem by oblivious mobile robots in infinite grids 遗忘型移动机器人在无限网格中的停车问题

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-31 DOI: 10.1016/j.tcs.2024.114953

Abhinav Chakraborty , Krishnendu Mukhopadhyaya

In this paper, the parking problem of a swarm of mobile robots has been studied. The robots are deployed at the nodes of an infinite grid, which has a subset of prefixed nodes marked as parking nodes. A parking node

p_{i}

has a capacity of

k_{i}

, which is given as an input and represents the number of robots it is capable of accommodating. As a solution to the parking problem, in the final configuration, robots need to partition themselves into groups so that each parking node contains a number of robots that are equal to the capacity of the node. It is assumed that the number of robots in the initial configuration equals the sum of the capacities of the parking nodes. The robots are assumed to be autonomous, anonymous, homogeneous, identical and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on the coordinate axes, nor do they agree on a common chirality. All the initial configurations for which the problem is unsolvable have been identified. A deterministic distributed algorithm has been proposed for the remaining configurations, ensuring the solvability of the problem.

本文研究了移动机器人群的停车问题。机器人被部署在一个无限网格的节点上，该网格有一个被标记为停车节点的前置节点子集。停车节点 pi 的容量为 ki，这是一个输入值，代表它能容纳的机器人数量。作为停车问题的解决方案，在最终配置中，机器人需要将自己分成若干组，以便每个停车节点包含的机器人数量与该节点的容量相等。假设初始配置中的机器人数量等于停车节点的容量总和。假设机器人是自主的、匿名的、同质的、相同的和遗忘的。它们在异步调度程序下运行。它们在坐标轴上没有任何共识，也没有共同的手性。所有无法解决问题的初始配置都已确定。针对其余配置提出了一种确定性分布式算法，确保了问题的可解决性。

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引用次数: 0

Double declined subnetwork reliability analysis in bubble-sort networks under node fault model 节点故障模型下气泡排序网络中的双衰落子网络可靠性分析

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-29 DOI: 10.1016/j.tcs.2024.114941

Kaiyue Meng, Yuxing Yang

The n-dimensional bubble-sort network

B_{n}

is a competitive interconnection network that could be used to construct large-scale multiprocessor computer systems. Let p be the reliability of each node in

B_{n}

and let

R_{n, n - 2} (p)

be the

B_{n - 2}

-subnetwork reliability (i.e., double declined subnetwork reliability) in

B_{n}

under the equiprobability node fault model. In this paper, the bounds on

R_{n, n - 2} (p)

are derived for

n \geq 4

, and an algorithm is given to further verify the accuracy of the lower and upper bounds. The MTTFs that maintain the healthy state of different numbers of disjoint

B_{n - 2}

's in

B_{n}

under different partition patterns are calculated. Simulations are also carried out to verify the MTTFs. Both the theoretical result and the simulating result show that using the flexible partition pattern will make the network more reliable in the sense of double declined subnetwork availability.

n 维气泡排序网络 Bn 是一种有竞争力的互连网络，可用于构建大型多处理器计算机系统。设 p 为 Bn 中每个节点的可靠性，设 Rn,n-2(p) 为等概率节点故障模型下 Bn 的 Bn-2 子网络可靠性（即双下降子网络可靠性）。本文推导了 n≥4 时 Rn,n-2(p) 的边界，并给出了进一步验证下边界和上边界准确性的算法。计算了在不同分区模式下，Bn 中不同数量的不相邻 Bn-2 保持健康状态的 MTTF。同时还进行了仿真以验证 MTTF。理论结果和仿真结果都表明，使用灵活的分区模式将使网络在双倍降低子网络可用性的意义上更加可靠。

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引用次数: 0