Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献_第9页

Approximating Maximin Share Allocations 近似最大份额分配

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-01-01 DOI: 10.4230/OASIcs.SOSA.2019.20

J. Garg, Patricia C. McGlaughlin, Setareh Taki

{"title":"Approximating Maximin Share Allocations","authors":"J. Garg, Patricia C. McGlaughlin, Setareh Taki","doi":"10.4230/OASIcs.SOSA.2019.20","DOIUrl":"https://doi.org/10.4230/OASIcs.SOSA.2019.20","url":null,"abstract":"We study the problem of fair allocation of M indivisible items among N agents using the popular notion of maximin share as our measure of fairness. The maximin share of an agent is the largest value she can guarantee herself if she is allowed to choose a partition of the items into N bundles (one for each agent), on the condition that she receives her least preferred bundle. A maximin share allocation provides each agent a bundle worth at least their maximin share. While it is known that such an allocation need not exist [Procaccia and Wang, 2014; Kurokawa et al., 2016], a series of work [Procaccia and Wang, 2014; David Kurokawa et al., 2018; Amanatidis et al., 2017; Barman and Krishna Murthy, 2017] provided 2/3 approximation algorithms in which each agent receives a bundle worth at least 2/3 times their maximin share. Recently, [Ghodsi et al., 2018] improved the approximation guarantee to 3/4. Prior works utilize intricate algorithms, with an exception of [Barman and Krishna Murthy, 2017] which is a simple greedy solution but relies on sophisticated analysis techniques. In this paper, we propose an alternative 2/3 maximin share approximation which offers both a simple algorithm and straightforward analysis. In contrast to other algorithms, our approach allows for a simple and intuitive understanding of why it works.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"1 1","pages":"20:1-20:11"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84069918","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: 55

On Primal-Dual Circle Representations 关于原始-对偶圆表示

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-01-01 DOI: 10.4230/OASIcs.SOSA.2019.8

S. Felsner, G. Rote

引用次数: 10

Simple Contention Resolution via Multiplicative Weight Updates 通过乘法权重更新的简单争用解决

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-01-01 DOI: 10.4230/OASIcs.SOSA.2019.16

Yi-Jun Chang, Wenyu Jin, S. Pettie

{"title":"Simple Contention Resolution via Multiplicative Weight Updates","authors":"Yi-Jun Chang, Wenyu Jin, S. Pettie","doi":"10.4230/OASIcs.SOSA.2019.16","DOIUrl":"https://doi.org/10.4230/OASIcs.SOSA.2019.16","url":null,"abstract":"We consider the classic contention resolution problem, in which devices conspire to share some common resource, for which they each need temporary and exclusive access. To ground the discussion, suppose (identical) devices wake up at various times, and must send a single packet over a shared multiple-access channel. In each time step they may attempt to send their packet; they receive ternary feedback {0, 1, 2+} from the channel, 0 indicating silence (no one attempted transmission), 1 indicating success (one device successfully transmitted), and 2+ indicating noise. We prove that a simple strategy suffices to achieve a channel utilization rate of 1/e − O( ), for any > 0. In each step, device i attempts to send its packet with probability pi, then applies a rudimentary multiplicative weight-type update to pi. pi ←  pi · e upon hearing silence (0) pi upon hearing success (1) pi · e− /(e−2) upon hearing noise (2+) This scheme works well even if the introduction of devices/packets is adversarial, and even if the adversary can jam time slots (make noise) at will. We prove that if the adversary jams J time slots, then this scheme will achieve channel utilization 1/e− , excluding O(J) wasted slots. Results similar to these (Bender, Fineman, Gilbert, Young, SODA 2016) were already achieved, but with a lower constant efficiency (less than 0.05) and a more complex algorithm. 2012 ACM Subject Classification Networks → Network protocols, Mathematics of computing → Probabilistic algorithms","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"4 1","pages":"16:1-16:16"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88816300","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: 12

A New Application of Orthogonal Range Searching for Computing Giant Graph Diameters 正交范围搜索在计算巨图直径中的新应用

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-12-18 DOI: 10.4230/OASIcs.SOSA.2019.12

G. Ducoffe

引用次数: 16

Simple Concurrent Labeling Algorithms for Connected Components 连接组件的简单并发标记算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-12-14 DOI: 10.4230/OASIcs.SOSA.2019.3

S. Liu, R. Tarjan

引用次数: 3

Towards a Unified Theory of Sparsification for Matching Problems 关于匹配问题的统一稀疏化理论

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-11-05 DOI: 10.4230/OASIcs.SOSA.2019.11

Sepehr Assadi, A. Bernstein

{"title":"Towards a Unified Theory of Sparsification for Matching Problems","authors":"Sepehr Assadi, A. Bernstein","doi":"10.4230/OASIcs.SOSA.2019.11","DOIUrl":"https://doi.org/10.4230/OASIcs.SOSA.2019.11","url":null,"abstract":"In this paper, we present a construction of a `matching sparsifier', that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to obtain several new algorithmic results for the maximum matching problem: \u0000* An almost $(3/2)$-approximation one-way communication protocol for the maximum matching problem, significantly simplifying the $(3/2)$-approximation protocol of Goel, Kapralov, and Khanna (SODA 2012) and extending it from bipartite graphs to general graphs. \u0000* An almost $(3/2)$-approximation algorithm for the stochastic matching problem, improving upon and significantly simplifying the previous $1.999$-approximation algorithm of Assadi, Khanna, and Li (EC 2017). \u0000* An almost $(3/2)$-approximation algorithm for the fault-tolerant matching problem, which, to our knowledge, is the first non-trivial algorithm for this problem. \u0000Our matching sparsifier is obtained by proving new properties of the edge-degree constrained subgraph (EDCS) of Bernstein and Stein (ICALP 2015; SODA 2016)---designed in the context of maintaining matchings in dynamic graphs---that identifies EDCS as an excellent choice for a matching sparsifier. This leads to surprisingly simple and non-technical proofs of the above results in a unified way. Along the way, we also provide a much simpler proof of the fact that an EDCS is guaranteed to contain a large matching, which may be of independent interest.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"7 1","pages":"11:1-11:20"},"PeriodicalIF":0.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80075260","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: 44

Submodular Optimization in the MapReduce Model MapReduce模型中的子模块优化

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-10-02 DOI: 10.4230/OASIcs.SOSA.2019.18

Paul Liu, J. Vondrák

引用次数: 25

Compressed Sensing with Adversarial Sparse Noise via L1 Regression 基于L1回归的对抗稀疏噪声压缩感知

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-09-01 DOI: 10.4230/OASIcs.SOSA.2019.19

Sushrut Karmalkar, Eric Price

引用次数: 31

Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems 放松Voronoi:终端聚类问题的一个简单框架

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-09-01 DOI: 10.4230/OASIcs.SOSA.2019.10

Arnold Filtser, Robert Krauthgamer, Ohad Trabelsi

{"title":"Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems","authors":"Arnold Filtser, Robert Krauthgamer, Ohad Trabelsi","doi":"10.4230/OASIcs.SOSA.2019.10","DOIUrl":"https://doi.org/10.4230/OASIcs.SOSA.2019.10","url":null,"abstract":"We reprove three known algorithmic bounds for terminal-clustering problems, using a single framework that leads to simpler proofs. In this genre of problems, the input is a metric space $(X,d)$ (possibly arising from a graph) and a subset of terminals $Ksubset X$, and the goal is to partition the points $X$ such that each part, called a cluster, contains exactly one terminal (possibly with connectivity requirements) so as to minimize some objective. The three bounds we reprove are for Steiner Point Removal on trees [Gupta, SODA 2001], for Metric $0$-Extension in bounded doubling dimension [Lee and Naor, unpublished 2003], and for Connected Metric $0$-Extension [Englert et al., SICOMP 2014]. \u0000A natural approach is to cluster each point with its closest terminal, which would partition $X$ into so-called Voronoi cells, but this approach can fail miserably due to its stringent cluster boundaries. A now-standard fix, which we call the Relaxed-Voronoi framework, is to use enlarged Voronoi cells, but to obtain disjoint clusters, the cells are computed greedily according to some order. This method, first proposed by Calinescu, Karloff and Rabani [SICOMP 2004], was employed successfully to provide state-of-the-art results for terminal-clustering problems on general metrics. However, for restricted families of metrics, e.g., trees and doubling metrics, only more complicated, ad-hoc algorithms are known. Our main contribution is to demonstrate that the Relaxed-Voronoi algorithm is applicable to restricted metrics, and actually leads to relatively simple algorithms and analyses.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"68 1","pages":"10:1-10:14"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83192228","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: 15

One (more) line on the most Ancient Algorithm in History 在历史上最古老的算法上再多说一行

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-08-23 DOI: 10.1137/1.9781611976014.3

Ilya Volkovich

引用次数: 2