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Guest editorial - Fun with algorithms 2024 客座编辑- 2024年算法的乐趣
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-03 DOI: 10.1016/j.tcs.2026.115742
Paolo Boldi , Giuseppe Prencipe , Tami Tamir
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引用次数: 0
Strategy-proof budgeting via a VCG-like mechanism 通过类似vcg的机制进行无策略预算
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-03 DOI: 10.1016/j.tcs.2025.115720
Jonathan Wagner, Reshef Meir
We present a strategy-proof public goods budgeting mechanism where agents determine both the total volume of expanses and the specific allocation. It is constructed as a modification of VCG to a non-typical environment, namely where we do not assume quasi-linear utilities nor direct revelation. We further show that under plausible assumptions it satisfies strategyproofness in strictly dominant strategies, and consequently implements the social optimum as a Coalition-Proof Nash Equilibrium. A primary (albeit not an exclusive) motivation of our model is Participatory Budgeting, where members of a community collectively decide the spending policy of public tax dollars. While incentives alignment in our mechanism, as in classic VCG, is achieved via individual payments we charge from agents, in a PB context that seems unreasonable. Our second main result thus provides that, under further specifications relevant in that context, these payments will vanish in large populations. In the last section we expand the mechanism’s definition to a class of mechanisms in which the designer can prioritize certain outcomes she sees as desirable. In particular we give the example of favoring equitable/egalitarian allocations.
我们提出了一种不受策略约束的公共产品预算机制,在这种机制中,代理人既决定扩张的总量,也决定具体的分配。它是作为VCG对非典型环境的修改而构建的,即我们不假设拟线性效用或直接启示。我们进一步证明,在合理的假设下,它满足严格优势策略的策略证明性,从而实现社会最优作为防联盟纳什均衡。我们模型的主要(尽管不是唯一)动机是参与式预算,即社区成员集体决定公共税收的支出政策。虽然在我们的机制中,如在经典的VCG中,激励机制是通过我们向代理商收取的个人费用来实现的,但在PB环境中,这似乎是不合理的。因此,我们的第二个主要结果是,根据与此有关的进一步规范,这些付款将在大量人口中消失。在最后一节中,我们将机制的定义扩展为一类机制,在这些机制中,设计师可以优先考虑她认为理想的某些结果。我们特别举出赞成公平/平等分配的例子。
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引用次数: 0
The category of H-posets h -集的范畴
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-02 DOI: 10.1016/j.tcs.2025.115725
Xiangping Chu, Qingguo Li
In this paper, we investigate the product of H-posets and their function spaces. Our main result establishes that the function space [X → Y], consisting of all Scott continuous functions from X to Y, is an H-poset when X is a continuous poset and Y is an H-poset with a smallest element. This finding generalizes earlier results reported by Kou, Liu, and Luo. Building on these insights, we derive a cartesian closed full subcategory of posets and Scott continuous functions. Additionally, we prove that the finite product of meet continuous H-posets remains a meet continuous H-poset.
本文研究了h -偏集及其函数空间的积。我们的主要结果证明,当X是连续偏序集,Y是最小元素的h偏序集时,由X到Y的所有Scott连续函数组成的函数空间[X → Y]是一个h偏序集。这一发现概括了之前由Kou、Liu和Luo报道的结果。在这些见解的基础上,我们推导出了偏置集和斯科特连续函数的笛卡儿闭完整子范畴。此外,我们证明了满足连续h -偏集的有限积仍然是满足连续h -偏集。
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引用次数: 0
On the detection of local and global amoebas: Theoretical insights and practical algorithms 关于局部和全局阿米巴虫的检测:理论见解和实用算法
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-02 DOI: 10.1016/j.tcs.2025.115730
Marcos E. González Laffitte , René González-Martínez , Amanda Montejano
We study local and global amoebas, which are graphs that have unique properties with respect to interpolation techniques in graphs. Our work includes a proof that almost every graph is not an amoeba, and the identification of a special type of edge-replacement called weird-edge-replacements. Additionally, we provide an infinite family of trees that are both weird local and global amoebas. Our contributions extend to the development and implementation of several algorithms for detecting local and global amoebas, which are made available in a public repository along with multiple examples.
我们研究了局部和全局阿米巴,它们是在图的插值技术方面具有独特性质的图。我们的工作包括证明几乎每个图都不是变形虫,以及识别一种特殊类型的边替换称为奇异边替换。此外,我们提供了一个无限的树家族,既有奇怪的本地变形虫,也有全球变形虫。我们的贡献扩展到开发和实现用于检测本地和全局阿米巴虫的几种算法,这些算法与多个示例一起在公共存储库中提供。
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引用次数: 0
Completely independent spanning trees in the line graph of complete multipartite graphs 完全多部图的线形图中的完全独立生成树
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-02 DOI: 10.1016/j.tcs.2025.115741
Hao Wang, Yan Wang, Baolei Cheng, Jianxi Fan
Spanning trees T1,T2,,Tt are completely independent spanning trees (CISTs) if and only if they are edge-disjoint and each node is internal in at most one tree. CISTs have a wide range of applications in routing protection, data transmission, etc., and can improve reliability, fault tolerance, and information security. Line graphs have received increasing attention in recent years for the construction of multiple CISTs, as they are more likely to satisfy the structural conditions required for their existence. This paper introduces an algorithm for constructing multiple CISTs in the line graph of the complete tripartite graph Kn3,n2,n1 (denoted by L(Kn3,n2,n1)), using multiple two-dimensional matrices to guide the construction process. Furthermore, it presents a method for constructing multiple CISTs in the line graph of the complete multipartite graph Knφ,nφ1,,n1 (denoted by L(Knφ,nφ1,,n1), when φ ≥ 4), utilizing edge-disjoint Hamiltonian cycles of the complete graph. In our simulation study, we employed multiple CISTs as transmission paths and compared their performance with shortest-path routing in terms of transmission latency and resilience to node failures.
生成树T1,T2,…,Tt是完全独立的生成树(cist),当且仅当它们是边不相交的,且每个节点最多在一个树的内部。cist在路由保护、数据传输等方面有着广泛的应用,可以提高可靠性、容错能力和信息安全性。近年来,线形图在构建多个cist方面受到越来越多的关注,因为它们更有可能满足其存在所需的结构条件。本文介绍了一种在完全三部图Kn3,n2,n1(记为L(Kn3,n2,n1))的线形图中构造多个cist的算法,该算法利用多个二维矩阵来指导构造过程。在此基础上,提出了利用完备图的边不相交哈密顿环,在完备多部图Knφ,nφ−1,…,n1(当φ ≥ 4时,记为L(Knφ,nφ−1,…,n1)的线图中构造多个cist的方法。在我们的模拟研究中,我们采用了多个cist作为传输路径,并比较了它们在传输延迟和节点故障恢复方面与最短路径路由的性能。
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引用次数: 0
Anonymous adversarial dynamic networks with logarithmic memory and communication 具有对数记忆和通信的匿名对抗动态网络
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-02 DOI: 10.1016/j.tcs.2025.115740
Dariusz R. Kowalski , Miguel A. Mosteiro
In seminal work on Adversarial Dynamic Networks, Kuhn, Lynch and Oshman (STOC 2010) [19] studied dynamic networks in which links are selected by an adversary and the number of network nodes is initially unknown. In such networks, they showed upper and lower bounds for computing the size of the network and any computable function of the nodes initial inputs. In this work, we address the same question in dynamic networks which additionally are: anonymous, possibly disconnected, and where internal memory and links’ bandwith are logarithmically limited. In the above framework, we study a fundamental communication principle – the All-to-all problem: each node has an input message to be delivered to all other nodes. (Once a node receives all inputs, any function can be computed locally.) Because of anonymity, each node needs to receive only a set of all input messages, each accompanied by a number of their initiating nodes (message multiplicity). We prove that this can be done deterministically in time proportional to the total number of messages’ bits multiplied by a small polynomial in networks’ parameters – namely, in the (initially unknown) number of nodes n and in the lower bound on the isoperimetric numbers of dynamically evolving graphs imin. Our results prove that a polynomial bit-throughput is possible in adversarial and anonymous dynamic networks with logarithmically limited bandwidth and internal memory.
在对抗性动态网络的开创性工作中,Kuhn, Lynch和Oshman (STOC 2010)研究了动态网络,其中链路由对手选择,网络节点的数量最初是未知的。在这样的网络中,他们展示了计算网络大小和节点初始输入的任何可计算函数的上界和下界。在这项工作中,我们在动态网络中解决了同样的问题,这些网络另外是:匿名的,可能断开连接的,并且内部存储器和链路的带宽是对数限制的。在上述框架中,我们研究了一个基本的通信原则——全对全问题:每个节点都有一个输入消息要传递给所有其他节点。(一旦节点接收到所有输入,任何函数都可以在本地计算。)由于匿名性,每个节点只需要接收所有输入消息的一组,每个输入消息都伴随着许多初始节点(消息多重性)。我们证明,这可以在与消息的总比特数乘以网络参数中的一个小多项式的时间成正比的情况下确定性地完成-即(最初未知的)节点数n和动态进化图的等周数imin的下界。我们的结果证明,在对数限制带宽和内存的对抗和匿名动态网络中,多项式比特吞吐量是可能的。
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引用次数: 0
On some 2-binomial coefficients of binary words: geometrical interpretation, partitions of integers, and fair words 二元词的2-二项式系数:几何解释、整数分割和公平词
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2026-01-01 DOI: 10.1016/j.tcs.2025.115732
Gwenaël Richomme
The binomial notation (wu) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (wab) and (wba) when a and b are distinct letters. We then study the structure of the 2-binomial equivalence class of a binary word w (two words are 2-binomially equivalent if they have the same binomial coefficients, that is, the same numbers of occurrences, for each word of length at most 2). Especially we prove the existence of an isomorphism between the graph of the 2-binomial equivalence class of w with respect to a particular rewriting rule and the lattice of partitions of the integer (wab) with (wa) parts and greatest part bounded by (wb). Finally we study binary fair words, the words over {a, b} having the same numbers of occurrences of ab and ba as subwords ((wab)=(wba)). In particular, we prove a recent conjecture related to a special case of the least square approximation.
二项表示法(wu)表示单词u作为w中的一个(分散的)子词出现的次数。我们首先介绍并研究当a和b是不同的字母时(wab)和(wba)的几何解释的可能用途。然后,我们研究了二进制词w的2-二项式等价类的结构(如果两个词具有相同的二项式系数,即每个长度最多为2的词的出现次数相同,则两个词是2-二项式等价的)。特别证明了w关于特定改写规则的2-二项式等价类的图与有(wa)个部分和最大部以(wb)为界的整数(wab)的分区格之间存在同构。最后,我们研究二元公平词,在{a, b}上的词与子词((wab)=(wba))具有相同的ab和ba的出现次数。特别地,我们证明了最近关于最小二乘近似的一个特殊情况的一个猜想。
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引用次数: 0
Hackenforb the chameleon: A game capable of mimicking (practically) any misère game Hackenforb the chameleon:一款能够模仿(实际上)任何错误游戏的游戏
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2025-12-31 DOI: 10.1016/j.tcs.2025.115731
Bojan Bašić , Danijela Popović
We consider the game Hackenforb, which has been introduced recently and for which it has been shown that it is capable of mimicking a vast spectrum of impartial combinatorial games. We show that it is capable of mimicking any game that has the property that from every position there exists a move to an ending position; for misère play, this amounts to any game in which the players are entitled to resign the game on any move.
我们以最近推出的游戏《Hackenforb》为例,它已经被证明能够模仿大量公正的组合游戏。我们证明了它能够模仿任何具有从每个位置到结束位置存在移动的属性的游戏;对于mis玩法,这是指玩家有权在任何移动中退出游戏的任何游戏。
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引用次数: 0
Parameterized complexity of fair many-to-one matchings 公平多对一匹配的参数化复杂度
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2025-12-31 DOI: 10.1016/j.tcs.2025.115727
Ramin Javadi, Hossein Shokouhi
Given a bipartite graph G=(UV,E), a left-perfect many-to-one matching is a subset ME such that each vertex in U is incident with exactly one edge in M. If U is partitioned into some groups, the matching is called fair if for every v ∈ V, the difference between the number of vertices matched with v in any two groups does not exceed a given threshold. In this paper, we investigate parameterized complexity of the fair left-perfect many-to-one matching problem with respect to the structural parameters of the input graph. In particular, we prove that the problem is W[1]-hard with respect to the feedback vertex number, tree-depth and the maximum degree of U, combined. Also, it is W[1]-hard with respect to the path-width, the number of groups and the maximum degree of U, combined. On the positive side, we prove that the problem is FPT with respect to the treewidth and the maximum degree of V. Also, it is FPT with respect to the neighborhood diversity of the input graph (which implies being FPT with respect to the vertex cover number and modular-width). Finally, we prove that the problem is FPT with respect to the tree-depth and the number of groups.
给定一个二部图G=(U∪V,E),一个左完全多对一匹配是一个子集M∈E,满足U中的每个顶点恰好与M中的一条边关联。如果将U划分为若干组,则对于每个V ∈ V,任意两组中与V匹配的顶点数之差不超过给定阈值,则称为公平匹配。本文研究了关于输入图结构参数的公平左完美多对一匹配问题的参数化复杂度。特别地,我们在反馈顶点数、树深度和U的最大度的组合方面证明了问题是W[1]-hard。对于路径宽度、组数和U的最大程度的组合,W[1]-hard。在积极的方面,我们证明了这个问题是关于树宽度和v的最大度的FPT,而且它是关于输入图的邻域多样性的FPT(这意味着是关于顶点覆盖数和模宽度的FPT)。最后,我们证明了该问题是关于树深度和组数的FPT问题。
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引用次数: 0
The parameterized complexity landscape of two-sets cut-uncut 两组切割-未切割的参数化复杂性景观
IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2025-12-30 DOI: 10.1016/j.tcs.2025.115726
Matthias Bentert , Fedor V. Fomin , Fanny Hauser , Saket Saurabh
In Two-Sets Cut-Uncut, we are given an undirected graph G=(V,E) and two terminal sets S and T. The task is to find a minimum cut C in G (if there is any) separating S from T under the following “uncut” condition. In the graph (V, EC), the terminals in each terminal set remain in the same connected component. In spite of the superficial similarity to the classic problem Minimum s-t-Cut, Two-Sets Cut-Uncut is computationally challenging. In particular, even deciding whether such a cut of any size exists, is already NP-complete. We initiate a systematic study of Two-Sets Cut-Uncut within the context of parameterized complexity. By leveraging known relations between many well-studied graph parameters, we characterize the structural properties of input graphs that allow for polynomial kernels, fixed-parameter tractability (FPT), and slicewise polynomial algorithms (XP). Our main contribution is the near-complete establishment of the complexity of these algorithmic properties within the described hierarchy of graph parameters.
On a technical level, our main results are fixed-parameter tractability for the (vertex-deletion) distance to cographs and an OR-cross composition excluding polynomial kernels for the vertex cover number of the input graph (under the standard complexity assumption NP ¬ coNP/poly).
在两集切割-未切割中,我们给定一个无向图G=(V,E)和两个终端集S和T。任务是在以下“未切割”条件下,在G中找到一个最小切割C(如果存在),将S与T分开。在图(V, E∈C)中,每个终端集中的终端保持在同一个连通分量中。尽管表面上与经典的最小s-t切问题相似,但两集切-非切问题在计算上具有挑战性。特别是,即使决定是否存在任何规模的削减,也已经是np完备的。在参数化复杂性的背景下,对两集切-非切问题进行了系统的研究。通过利用许多经过充分研究的图参数之间的已知关系,我们描述了允许多项式核、固定参数可跟踪性(FPT)和分段多项式算法(XP)的输入图的结构属性。我们的主要贡献是在描述的图参数层次结构中几乎完全建立了这些算法属性的复杂性。在技术层面上,我们的主要成果是到图的(顶点删除)距离的固定参数可追溯性和输入图的顶点覆盖数的不含多项式核的or交叉组合(在标准复杂性假设NP¬coNP/poly下)。
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引用次数: 0
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Theoretical Computer Science
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