arXiv - CS - Data Structures and Algorithms最新文献_第4页

MATWA: A Web Toolkit for Matching under Preferences MATWA：根据偏好进行匹配的网络工具包

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-06 DOI: arxiv-2409.04402

Frederik Glitzner, David Manlove

引用次数: 0

FPT Algorithms using Minimal Parameters for a Generalized Version of Maximin Shares 使用最小参数的 FPT 算法，适用于 Maximin Shares 的广义版本

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-06 DOI: arxiv-2409.04225

Klaus Jansen, Alexandra Lassota, Malte Tutas, Adrian Vetta

{"title":"FPT Algorithms using Minimal Parameters for a Generalized Version of Maximin Shares","authors":"Klaus Jansen, Alexandra Lassota, Malte Tutas, Adrian Vetta","doi":"arxiv-2409.04225","DOIUrl":"https://doi.org/arxiv-2409.04225","url":null,"abstract":"We study the computational complexity of fairly allocating indivisible,\u0000mixed-manna items. For basic measures of fairness, this problem is hard in\u0000general. Thus, research has flourished concerning input classes where efficient\u0000algorithms exist, both for the purpose of establishing theoretical boundaries\u0000and for the purpose of designing practical algorithms for real-world instances.\u0000Notably, the paradigm of fixed-parameter tractability (FPT) has lead to new\u0000insights and improved algorithms for a variety of fair allocation problems;\u0000see, for example, Bleim et al. (IJCAI 16), Aziz et al. (AAAI 17), Bredereck et\u0000al. (EC 19) and Kulkarni et al. (EC 21). Our focus is the fairness measure maximin shares (MMS). Motivated by the\u0000general non-existence of MMS allocations, Aziz et al. (AAAI 17) studied optimal\u0000MMS allocations, namely solutions that achieve the best $alpha$-approximation\u0000for the maximin share value of every agent. These allocations are guaranteed to\u0000exist, prompting the important open question of whether optimal MMS allocations\u0000can be computed efficiently. We answer this question affirmatively by providing\u0000FPT algorithms to output optimal MMS allocations. Furthermore, our techniques\u0000extend to find allocations that optimize alternative objectives, such as\u0000minimizing the additive approximation, and maximizing some variants of global\u0000welfare. In fact, all our algorithms are designed for a more general MMS problem in\u0000machine scheduling. Here, each mixed-manna item (job) must be assigned to an\u0000agent (machine) and has a processing time and a deadline. We develop efficient\u0000algorithms running in FPT time. Formally, we present polynomial time algorithms\u0000w.r.t. the input size times some function dependent on the parameters that\u0000yield optimal maximin-value approximations (among others) when parameterized by\u0000a set of natural parameters","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202651","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: 0

RCM++:Reverse Cuthill-McKee ordering with Bi-Criteria Node Finder RCM++：利用双标准节点查找器进行反向 Cuthill-McKee 排序

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-06 DOI: arxiv-2409.04171

JiaJun Hou, HongJie Liu, ShengXin Zhu

{"title":"RCM++:Reverse Cuthill-McKee ordering with Bi-Criteria Node Finder","authors":"JiaJun Hou, HongJie Liu, ShengXin Zhu","doi":"arxiv-2409.04171","DOIUrl":"https://doi.org/arxiv-2409.04171","url":null,"abstract":"The Reverse Cuthill-McKee (RCM) algorithm is a graph-based method for\u0000reordering sparse matrices, renowned for its effectiveness in minimizing matrix\u0000bandwidth and profile. This reordering enhances the efficiency of matrix\u0000operations, making RCM pivotal among reordering algorithms. In the context of\u0000executing the RCM algorithm, it is often necessary to select a starting node\u0000from the graph representation of the matrix. This selection allows the\u0000execution of BFS (Breadth-First Search) to construct the level structure. The\u0000choice of this starting node significantly impacts the algorithm's performance,\u0000necessitating a heuristic approach to identify an optimal starting node,\u0000commonly referred to as the RCM starting node problem. Techniques such as the\u0000minimum degree method and George-Liu (GL) algorithm are popular solutions. This paper introduces a novel algorithm addressing the RCM starting node\u0000problem by considering both the eccentricity and the width of the node during\u0000the run. Integrating this algorithm with the RCM algorithm, we introduce RCM++.\u0000Experimental results demonstrate that RCM++ outperforms existing RCM methods in\u0000major software libraries, achieving higher quality results with comparable\u0000computation time. This advancement fosters the further application and\u0000development of the RCM algorithm.The code related to this research has been\u0000made available at https://github.com/SStan1/RCM_PP.git.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202654","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: 0

Improving the Parameter Dependency for High-Multiplicity Scheduling on Uniform Machines 改进统一机器上高多任务调度的参数依赖性

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-06 DOI: arxiv-2409.04212

Klaus Jansen, Kai Kahler, Lis Pirotton, Malte Tutas

{"title":"Improving the Parameter Dependency for High-Multiplicity Scheduling on Uniform Machines","authors":"Klaus Jansen, Kai Kahler, Lis Pirotton, Malte Tutas","doi":"arxiv-2409.04212","DOIUrl":"https://doi.org/arxiv-2409.04212","url":null,"abstract":"We address scheduling problems on uniform machines with high-multiplicity\u0000encoding, introducing a divide and conquer approach to assess the feasibility\u0000of a general Load Balancing Problem (LBP). Via reductions, our algorithm can\u0000also solve the more well-known problems $Q|C_{max}$ (makespan minimization),\u0000$Q|C_{min}$ (santa claus) and $Q|C_{text{envy}}$ (envy minimization).\u0000State-of-the-art algorithms for these problems, e.g. by Knop et al. (Math.\u0000Program. '23), have running times with parameter dependency\u0000$p_{max}^{O(d^2)}$, where $p_{max}$ is the largest processing time and $d$ is\u0000the number of different processing times. We partially answer the question\u0000asked by Kouteck'y and Zink (ISAAC'20) about whether this quadratic dependency\u0000of $d$ can be improved to a linear one: Under the natural assumption that the\u0000machines are similar in a way that $s_{max}/s_{min} leq p_{max}^{O(1)}$ and\u0000$tauleq p_{max}^{O(1)}$, our proposed algorithm achieves parameter\u0000dependency $p_{max}^{O(d)}$ for the problems\u0000${Q|{C_{max},C_{min},C_{text{envy}}}}$. Here, $tau$ is the number of\u0000distinct machine speeds. Even without this assumption, our running times\u0000achieve a state-of-the-art parameter dependency and do so with an entirely\u0000different approach.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202653","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: 0

Constant Approximating Disjoint Paths on Acyclic Digraphs is W[1]-hard 常量逼近无循环图上的不相交路径是 W[1]-hard

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-05 DOI: arxiv-2409.03596

Michał Włodarczyk

引用次数: 0

Fine-Grained Equivalence for Problems Related to Integer Linear Programming 整数线性规划相关问题的细粒度等价性

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-05 DOI: arxiv-2409.03675

Lars Rohwedder, Karol Węgrzycki

{"title":"Fine-Grained Equivalence for Problems Related to Integer Linear Programming","authors":"Lars Rohwedder, Karol Węgrzycki","doi":"arxiv-2409.03675","DOIUrl":"https://doi.org/arxiv-2409.03675","url":null,"abstract":"Integer Linear Programming with $n$ binary variables and $m$ many\u0000$0/1$-constraints can be solved in time $2^{tilde O(m^2)} text{poly}(n)$ and\u0000it is open whether the dependence on $m$ is optimal. Several seemingly\u0000unrelated problems, which include variants of Closest String, Discrepancy\u0000Minimization, Set Cover, and Set Packing, can be modelled as Integer Linear\u0000Programming with $0/1$ constraints to obtain algorithms with the same running\u0000time for a natural parameter $m$ in each of the problems. Our main result\u0000establishes through fine-grained reductions that these problems are equivalent,\u0000meaning that a $2^{O(m^{2-varepsilon})} text{poly}(n)$ algorithm with\u0000$varepsilon > 0$ for one of them implies such an algorithm for all of them. In the setting above, one can alternatively obtain an $n^{O(m)}$ time\u0000algorithm for Integer Linear Programming using a straightforward dynamic\u0000programming approach, which can be more efficient if $n$ is relatively small\u0000(e.g., subexponential in $m$). We show that this can be improved to\u0000${n'}^{O(m)} + O(nm)$, where $n'$ is the number of distinct (i.e.,\u0000non-symmetric) variables. This dominates both of the aforementioned running\u0000times.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202656","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: 0

Fast ($sim N$) Diffusion Map Algorithm 快速（$sim N$ ）扩散图算法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-05 DOI: arxiv-2409.05901

Julio Candanedo

引用次数: 0

Does Subset Sum Admit Short Proofs? 子集和允许简短证明吗？

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-05 DOI: arxiv-2409.03526

Michał Włodarczyk

引用次数: 0

Space-Efficient Algorithm for Integer Programming with Few Constraints 具有少量约束条件的整数编程空间效率算法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-05 DOI: arxiv-2409.03681

Lars Rohwedder, Karol Węgrzycki

引用次数: 0

Online Scheduling via Gradient Descent for Weighted Flow Time Minimization 通过梯度下降实现加权流时最小化的在线调度

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.03020

Qingyun Chen, Sungjin Im, Aditya Petety

{"title":"Online Scheduling via Gradient Descent for Weighted Flow Time Minimization","authors":"Qingyun Chen, Sungjin Im, Aditya Petety","doi":"arxiv-2409.03020","DOIUrl":"https://doi.org/arxiv-2409.03020","url":null,"abstract":"In this paper, we explore how a natural generalization of Shortest Remaining\u0000Processing Time (SRPT) can be a powerful emph{meta-algorithm} for online\u0000scheduling. The meta-algorithm processes jobs to maximally reduce the objective\u0000of the corresponding offline scheduling problem of the remaining jobs:\u0000minimizing the total weighted completion time of them (the residual optimum).\u0000We show that it achieves scalability for minimizing total weighted flow time\u0000when the residual optimum exhibits emph{supermodularity}. Scalability here\u0000means it is $O(1)$-competitive with an arbitrarily small speed augmentation\u0000advantage over the adversary, representing the best possible outcome achievable\u0000for various scheduling problems. Thanks to this finding, our approach does not require the residual optimum to\u0000have a closed mathematical form. Consequently, we can obtain the schedule by\u0000solving a linear program, which makes our approach readily applicable to a rich\u0000body of applications. Furthermore, by establishing a novel connection to\u0000emph{substitute valuations in Walrasian markets}, we show how to achieve\u0000supermodularity, thereby obtaining scalable algorithms for various scheduling\u0000problems, such as matroid scheduling, generalized network flow, and generalized\u0000arbitrary speed-up curves, etc., and this is the emph{first} non-trivial or\u0000scalable algorithm for many of them.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202658","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: 0