Theoretical Computer Science最新文献_第6页

Sink location problems in dynamic flow grid networks 动态流网格网络中的下沉点定位问题

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-09-03 DOI: 10.1016/j.tcs.2024.114812

{"title":"Sink location problems in dynamic flow grid networks","authors":"","doi":"10.1016/j.tcs.2024.114812","DOIUrl":"10.1016/j.tcs.2024.114812","url":null,"abstract":"<div>A dynamic flow network consists of a directed graph, where nodes called sources represent locations of evacuees, and nodes called sinks represent locations of evacuation facilities. Each source and each sink are given supply representing the number of evacuees and demand representing the maximum number of acceptable evacuees, respectively. Each edge is given capacity and transit time. Here, the capacity of an edge bounds the rate at which evacuees can enter the edge per unit time, and the transit time represents the time which evacuees take to travel across the edge. The evacuation completion time is the minimum time at which each evacuee can arrive at one of the evacuation facilities. Given a dynamic flow network without sinks, once sinks are located on some nodes or edges, the evacuation completion time for this sink location is determined. We then consider the problem of locating sinks to minimize the evacuation completion time, called the sink location problem. The problems have been given polynomial-time algorithms only for limited networks such as paths [1], [2], [3], cycles [1], and trees [4], [5], [6], but no polynomial-time algorithms are known for more complex network classes. In this paper, we prove that the 1-sink location problem can be solved in polynomial-time when an input network is a grid with uniform edge capacity and transit time.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

The cyclic diagnosability of balanced hypercubes under the PMC and MM⁎ model PMC和MM⁎模型下平衡超立方体的可循环诊断性

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114816

引用次数: 0

The Maximum Zero-Sum Partition problem 最大零和分割问题

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114811

引用次数: 0

On monochromatic arithmetic progressions in binary words associated with pattern sequences 论与模式序列相关的二进制词中的单色算术级数

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114815

{"title":"On monochromatic arithmetic progressions in binary words associated with pattern sequences","authors":"","doi":"10.1016/j.tcs.2024.114815","DOIUrl":"10.1016/j.tcs.2024.114815","url":null,"abstract":"<div>Let <math><msub><mrow><mi>e</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math> denote the number of occurrences of a fixed pattern v in the binary expansion of <math><mi>n</mi><mo>∈</mo><mi>N</mi></math>. In this paper we study monochromatic arithmetic progressions in the class of binary words <math><msub><mrow><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mn>2</mn><mo>)</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math>, which includes the famous Thue–Morse word t and Rudin–Shapiro word r. We prove that the length of a monochromatic arithmetic progression of difference <math><mi>d</mi><mo>≥</mo><mn>3</mn></math> starting at 0 in r is at most <math><mo>(</mo><mi>d</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>/</mo><mn>2</mn></math>, with equality for infinitely many d. We also compute the maximal length of a monochromatic arithmetic progression in r of difference <math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>−</mo><mn>1</mn></math> and <math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>+</mo><mn>1</mn></math>. For a general pattern v we show that the maximal length of a monochromatic arithmetic progression of difference d is at most linear in d. Moreover, we prove that a linear lower bound holds for suitable subsequences <math><msub><mrow><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></msub></math> of differences. We also offer a number of related problems and conjectures.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004328/pdfft?md5=f1b8c0a8a097177b0f698184130f8ee6&pid=1-s2.0-S0304397524004328-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142129146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

User-driven competitive influence maximization in social networks 社交网络中用户驱动的竞争影响力最大化

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114813

{"title":"User-driven competitive influence maximization in social networks","authors":"","doi":"10.1016/j.tcs.2024.114813","DOIUrl":"10.1016/j.tcs.2024.114813","url":null,"abstract":"<div>Online social networks have emerged as pivotal platforms where users not only interact but also influence each other's decisions and preferences. As these networks grow in complexity, understanding and leveraging influence dynamics within networks have become essential, particularly for businesses and marketers. Competitive Influence Maximization (CIM) in online social networks has garnered significant interest, focusing on maximizing influence spread among multiple entities. However, recent research on CIM often overlooks the differences in user preferences, which realistically impact the propagation of competitive influence. To address this issue, we introduce the User-Driven Competitive Linear Threshold (UDCLT) model. This model takes into account user preference differences for two distinct brands within the identical product category, thereby formulating the User-Driven Competitive Influence Maximization (UDCIM) problem. Based on community structure, we introduce a novel measure, namely Topology Importance (TI), to assess a node's potential influence within a social network by considering its connections within and across communities. To resolve the UDCIM problem effectively, we develop a novel two-phase algorithm, the Community-based Dual Influence Assessment (CDIA) algorithm, which integrates Topology Importance and Dual Influence to identify seed nodes. Various experiments are conducted on four real-world datasets, illustrating the efficiency and effectiveness of the CDIA algorithm in addressing the UDCIM problem.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Graph realization of distance sets 距离集的图形实现

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114810

{"title":"Graph realization of distance sets","authors":"","doi":"10.1016/j.tcs.2024.114810","DOIUrl":"10.1016/j.tcs.2024.114810","url":null,"abstract":"<div>The Distance Realization problem is defined as follows. Given an <math><mi>n</mi><mo>×</mo><mi>n</mi></math> matrix D of nonnegative integers, interpreted as inter-vertex distances, find an n-vertex weighted or unweighted graph G realizing D, i.e., whose inter-vertex distances satisfy <math><mi>d</mi><mi>i</mi><mi>s</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math> for every <math><mn>1</mn><mo>≤</mo><mi>i</mi><mo><</mo><mi>j</mi><mo>≤</mo><mi>n</mi></math>, or decide that no such realizing graph exists. The problem was studied for general weighted and unweighted graphs, as well as for cases where the realizing graph is restricted to a specific family of graphs (e.g., trees or bipartite graphs). An extension of Distance Realization that was studied in the past is where each entry in the matrix D may contain a range of consecutive permissible values. We refer to this extension as Range Distance Realization (or Range-DR). Restricting each range to at most k values yields the problem k-Range Distance Realization (or k-Range-DR). The current paper introduces a new extension of Distance Realization, in which each entry <math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math> of the matrix may contain an arbitrary set of acceptable values for the distance between i and j, for every <math><mn>1</mn><mo>≤</mo><mi>i</mi><mo><</mo><mi>j</mi><mo>≤</mo><mi>n</mi></math>. We refer to this extension as Set Distance Realization (Set-DR), and to the restricted problem where each entry may contain at most k values as k-Set Distance Realization (or k-Set-DR).We first show that 2-Range-DR is NP-hard for unweighted graphs (implying the same for 2-Set-DR). Next we prove that 2-Set-DR is NP-hard for unweighted and weighted trees.Finally, we explore Set-DR where the realization is restricted to the families of stars, paths, cycles, or caterpillars. For the weighted case, our positive results are that there exist polynomial time algorithms for the 2-Set-DR problem on stars, paths and cycles, and for the 1-Set-DR problem on caterpillars. On the hardness side, we prove that 6-Set-DR is NP-hard for stars and 5-Set-DR is NP-hard for paths, cycles and caterpillars. For the unweighted case, our results are the same, except for the case of unweighted stars, for which k-Set-DR is polynomially solvable for a","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

On submodular prophet inequalities and correlation gap 关于亚模态预言不等式和相关差距

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-30 DOI: 10.1016/j.tcs.2024.114814

{"title":"On submodular prophet inequalities and correlation gap","authors":"","doi":"10.1016/j.tcs.2024.114814","DOIUrl":"10.1016/j.tcs.2024.114814","url":null,"abstract":"<div>Prophet inequalities and secretary problems have been extensively studied in recent years due to their elegance, connections to online algorithms, stochastic optimization, and mechanism design problems in game theoretic settings. Rubinstein and Singla [31] developed a notion of combinatorial prophet inequalities in order to generalize the standard prophet inequality setting to combinatorial valuation functions such as submodular and subadditive functions. For non-negative submodular functions they demonstrated a constant factor prophet inequality for matroid constraints. Along the way they showed a variant of the correlation gap for non-negative submodular functions.In this paper we revisit their notion of correlation gap as well as the standard notion of correlation gap and prove much tighter and cleaner bounds. Via these bounds and other insights we obtain substantially improved constant factor combinatorial prophet inequalities for both monotone and non-monotone submodular functions over any constraint that admits an Online Contention Resolution Scheme. In addition to improved bounds we describe efficient polynomial-time algorithms that achieve these bounds.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

The diameter of sum basic equilibria games 和基本均衡博弈的直径

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-28 DOI: 10.1016/j.tcs.2024.114807

{"title":"The diameter of sum basic equilibria games","authors":"","doi":"10.1016/j.tcs.2024.114807","DOIUrl":"10.1016/j.tcs.2024.114807","url":null,"abstract":"<div>We study the sum basic network creation game introduced in 2010 by Alon, Demaine, Hajiaghai and Leighton. In this game, an undirected and unweighted graph G is said to be a sum basic equilibrium if and only if, for every edge uv and any vertex <math><msup><mrow><mi>v</mi></mrow><mrow><mo>′</mo></mrow></msup></math> in G, swapping edge uv with edge <math><mi>u</mi><msup><mrow><mi>v</mi></mrow><mrow><mo>′</mo></mrow></msup></math> does not decrease the total sum of the distances from u to all the other vertices. This concept lies at the heart of the network creation games, where the central problem is to understand the structure of the resulting equilibrium graphs, and in particular, how well they globally minimize the diameter. In this sense, in 2013 Alon et al. showed an upper bound of <math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><msqrt><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow></msqrt><mo>)</mo></mrow></msup></math> on the diameter of sum basic equilibria, and they also proved that if a sum basic equilibrium graph is a tree, then it has diameter at most 2. In this paper, we prove that the upper bound of 2 also holds for bipartite graphs and even for some non-bipartite classes like block graphs and cactus graphs.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004249/pdfft?md5=ab3c3a76dbdf1ff573755d82085be616&pid=1-s2.0-S0304397524004249-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Towards zero knowledge argument for double discrete logarithm with constant cost 以恒定成本实现双离散对数的零知识论证

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-26 DOI: 10.1016/j.tcs.2024.114799

引用次数: 0

Parameterised approximation of the fixation probability of the dominant mutation in the multi-type Moran process 多类型莫兰过程中显性突变固定概率的参数化近似值

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-22 DOI: 10.1016/j.tcs.2024.114785

{"title":"Parameterised approximation of the fixation probability of the dominant mutation in the multi-type Moran process","authors":"","doi":"10.1016/j.tcs.2024.114785","DOIUrl":"10.1016/j.tcs.2024.114785","url":null,"abstract":"<div>The multi-type Moran process is an evolutionary process on a connected graph G in which each vertex has one of k types and, in each step, a vertex v is chosen to reproduce its type to one of its neighbours. The probability of a vertex v being chosen for reproduction is proportional to the fitness of the type of v. So far, the literature was almost solely concerned with the 2-type Moran process in which each vertex is either healthy (type 0) or a mutant (type 1), and the main problem of interest has been the (approximate) computation of the so-called fixation probability, i.e., the probability that eventually all vertices are mutants.In this work we initiate the study of approximating fixation probabilities in the multi-type Moran process on general graphs. Our main result is an FPTRAS (fixed-parameter tractable randomised approximation scheme) for computing the fixation probability of the dominant mutation; the parameter is the number of types and their fitnesses. In the course of our studies we also provide novel upper bounds on the expected absorption time, i.e., the time that it takes the multi-type Moran process to reach a state in which each vertex has the same type.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142041213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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