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When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear-Time [article]

Sepehr Assadi, Shay Solomon
<span title="2020-06-13">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Maximal independent set (MIS), maximal matching (MM), and (Δ+1)-coloring in graphs of maximum degree Δ are among the most prominent algorithmic graph theory problems.  ...  In SODA 2019, Assadi, Chen, and Khanna gave a randomized algorithm for (Δ+1)-coloring that runs in O(n√(n)) time, which even for moderately dense graphs is sublinear in the input size.  ...  Theorem 3 now follows immediately from Lemma 5.2, which states that unless the algorithm makes Ω(n 2 ) queries, there always exists at least one graph in G n for which the output matching of the algorithm  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.07628v1">arXiv:2006.07628v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rpofttwyb5eedfhcx4a4zkwu4m">fatcat:rpofttwyb5eedfhcx4a4zkwu4m</a> </span>
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When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear Time

Sepehr Assadi, Shay Solomon, Michael Wagner
<span title="2019-07-08">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
Maximal independent set (MIS), maximal matching (MM), and (∆ + 1)-(vertex) coloring in graphs of maximum degree ∆ are among the most prominent algorithmic graph theory problems.  ...  In SODA 2019, Assadi, Chen, and Khanna gave a randomized algorithm for (∆ + 1)-coloring that runs in O(n √ n) time 1 , which even for moderately dense graphs is sublinear in the input size.  ...  However, as we show in Section 5 this and any other deterministic algorithm for MM, cannot run in sublinear-time even when β(G) = 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.17">doi:10.4230/lipics.icalp.2019.17</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/AssadiS19.html">dblp:conf/icalp/AssadiS19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/whugfltufrf65bx54u4mii6lke">fatcat:whugfltufrf65bx54u4mii6lke</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200220192739/https://drops.dagstuhl.de/opus/volltexte/2019/10593/pdf/LIPIcs-ICALP-2019-17.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/83/f5/83f54338f06f1cfd42faea04bb45965b05e005d2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Round Compression for Parallel Graph Algorithms in Strongly Sublinear Space [article]

Krzysztof Onak
<span title="2018-07-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our techniques are relatively simple and can also be used to accelerate the simulation of distributed algorithms for bounded-degree graphs and finding a maximal independent set in bounded-arboricity graphs  ...  We consider the task of computing a large matching or small vertex cover in this model when the space per machine is n^δ for δ∈ (0,1), where n is the number of vertices in the input graph.  ...  For instance, Brandt, Fischer, and Uitto [BFU18a] give an algorithm for computing a maximal independent set in trees.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.08745v1">arXiv:1807.08745v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rsyeiu2w7ze3lbcrh6tdccayty">fatcat:rsyeiu2w7ze3lbcrh6tdccayty</a> </span>
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Improved MPC Algorithms for MIS, Matching, and Coloring on Trees and Beyond

Mohsen Ghaffari, Christoph Grunau, Ce Jin, Hagit Attiya
<span title="2020-10-07">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2pcluxp32rfojgwekdrryxoaqu" style="color: black;">International Symposium on Distributed Computing</a> </i> &nbsp;
We present O(log log n) round scalable Massively Parallel Computation algorithms for maximal independent set and maximal matching, in trees and more generally graphs of bounded arboricity, as well as for  ...  Moreover, our matching algorithm is presumably optimal as its bound matches an Ω(log log n) conditional lower bound of Ghaffari, Kuhn, and Uitto [FOCS'19].  ...  For the strongly superlinear memory regime, Lattanzi et al. [27] presented O(1)-round algorithms for maximal matching and maximal independent set.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.disc.2020.34">doi:10.4230/lipics.disc.2020.34</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/wdag/GhaffariGJ20.html">dblp:conf/wdag/GhaffariGJ20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tghaqfzy3jbdbidjsqvb2cefpa">fatcat:tghaqfzy3jbdbidjsqvb2cefpa</a> </span>
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Improved MPC Algorithms for MIS, Matching, and Coloring on Trees and Beyond [article]

Mohsen Ghaffari, Christoph Grunau, Ce Jin
<span title="2020-08-10">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present O(loglog n) round scalable Massively Parallel Computation algorithms for maximal independent set and maximal matching, in trees and more generally graphs of bounded arboricity, as well as for  ...  Moreover, our matching algorithm is presumably optimal as its bound matches an Ω(loglog n) conditional lower bound of Ghaffari, Kuhn, and Uitto [FOCS'19].  ...  For the strongly superlinear memory regime, Lattanzi et al. [27] presented O(1)-round algorithms for maximal matching and maximal independent set.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.09610v2">arXiv:2002.09610v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nlvbvo7dyvekhbz5qgfm4biss4">fatcat:nlvbvo7dyvekhbz5qgfm4biss4</a> </span>
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Sublinear Algorithms and Lower Bounds for Metric TSP Cost Estimation [article]

Yu Chen, Sampath Kannan, Sanjeev Khanna
<span title="2020-06-09">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we make progress on both algorithms and lower bounds for estimating metric TSP cost.  ...  We consider the problem of designing sublinear time algorithms for estimating the cost of a minimum metric traveling salesman (TSP) tour.  ...  For any ε > 0, any single-pass streaming algorithm that is able to approximate the cost of graphic TSP of an input graph G within a factor of 2 − ε in insertion-only streams with probability at least 2  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.05490v1">arXiv:2006.05490v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yfsng2mzfzapjmf6uegzeqajyu">fatcat:yfsng2mzfzapjmf6uegzeqajyu</a> </span>
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Massively Parallel Symmetry Breaking on Sparse Graphs: MIS and Maximal Matching [article]

Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Richard M. Karp
<span title="2019-05-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, we consider symmetry breaking problems of maximal independent set (MIS) and maximal matching (MM), which are among the most intensively studied problems in distributed/parallel computing,  ...  We show that both MIS and MM admit O(√(α)·α + ^2 n) round algorithms using O(n^ϵ) space per machine for any constant ϵ∈ (0, 1) and using O(m) total space.  ...  Acknowledgements The authors would like to thank Saeed Seddighin for useful discussions and for bringing up the question of whether matching can be solved in sublogarithmic rounds of low-memory MPC.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.06701v3">arXiv:1807.06701v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pytfrwpus5gbnazt6qijy7zyg4">fatcat:pytfrwpus5gbnazt6qijy7zyg4</a> </span>
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Exponentially Faster Massively Parallel Maximal Matching [article]

Soheil Behnezhad, MohammadTaghi Hajiaghayi, David G. Harris
<span title="2019-10-16">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This, among some other results, leads to an O(loglogΔ) round algorithm for maximal matching with O(n) space (or even mildly sublinear in n using standard techniques).  ...  All known MPC algorithms for maximal matching either take polylogarithmic time which is considered inefficient, or require a strictly super-linear space of n^1+Ω(1) per machine.  ...  We summarize these properties in Appendix A. Property 3 was originally developed in the context of sublinear time algorithms for approximating maximum matching size.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.03744v3">arXiv:1901.03744v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xme6vq37urednp36yngzxnqor4">fatcat:xme6vq37urednp36yngzxnqor4</a> </span>
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Distributed Maximum Matching in Bounded Degree Graphs [article]

Guy Even, Moti Medina, Dana Ron
<span title="2014-11-11">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our algorithm for the edge-weighted case computes a matching whose weight is at least (1-) times the optimal in ({1/,n/})^O(1/)·(Δ^O(1/)+^*(n)) rounds for edge-weights in [,1].  ...  Our algorithm for the unweighted case computes a matching whose size is at least (1-) times the optimal in Δ^O(1/) + O(1/^2) ·^*(n) rounds where n is the number of vertices in the graph and Δ is the maximum  ...  The algorithm outputs whether q i is in I, for some maximal independent set I ⊆ V .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.7882v3">arXiv:1407.7882v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pliy7e2xerhnzntfdfmemwsrfu">fatcat:pliy7e2xerhnzntfdfmemwsrfu</a> </span>
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Best of Two Local Models: Local Centralized and Local Distributed Algorithms [article]

Guy Even, Moti Medina, Dana Ron
<span title="2014-11-11">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over  ...  We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms.  ...  MIS denotes maximal independent set, MM Table 2 : 2 A comparison between CENTLOCAL oracles in sub-linear approximation algorithms and our In the RAM model, the running time per query of our algorithms  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1402.3796v3">arXiv:1402.3796v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ub2t6c3gkrfenmt4wkknbuekzm">fatcat:ub2t6c3gkrfenmt4wkknbuekzm</a> </span>
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Sublinear-time parallel algorithms for matching and related problems

A.V. Goldberg, S.A. Plotkin, P.M. Vaidya
<span title="">1988</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science</a> </i> &nbsp;
This paper presents the rst sublinear-time deterministic parallel algorithms for bipartite matching and several related problems, including maximal node-disjoint paths, depth-rst search, and ows in zero-one  ...  In particular, we present sublinear-time deterministic parallel algorithms for nding a minimum-weight bipartite matching and for nding a minimum-cost ow in a network with zero-one capacities, if the weights  ...  The second author would like to thank Charles Leiserson for his enthusiastic support and encouragement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.1988.21935">doi:10.1109/sfcs.1988.21935</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/GoldbergPV88.html">dblp:conf/focs/GoldbergPV88</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/abq7v4u64ngdvdc7ixa5syanyi">fatcat:abq7v4u64ngdvdc7ixa5syanyi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190308091605/http://pdfs.semanticscholar.org/f071/0725e5c81a33f34653f534fefbfab7e68fc0.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f0/71/f0710725e5c81a33f34653f534fefbfab7e68fc0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.1988.21935"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Sublinear Algorithms for (Δ + 1) Vertex Coloring [article]

Sepehr Assadi, Yu Chen, Sanjeev Khanna
<span title="2019-01-05">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We answer this fundamental question in the affirmative for several canonical classes of sublinear algorithms including graph streaming, sublinear time, and massively parallel computation (MPC) algorithms  ...  No non-trivial sublinear time algorithms were known prior to our work. * A parallel algorithm in the massively parallel computation (MPC) model using Õ(n) memory per machine and O(1) MPC rounds.  ...  Acknowledgements The first author would like to thank Merav Parter for helpful comments and the pointer to [43] , and T.S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.08886v2">arXiv:1807.08886v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ktk53kt4bbe6nowmu3ylyxyrpu">fatcat:ktk53kt4bbe6nowmu3ylyxyrpu</a> </span>
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Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms

Michal Parnas, Dana Ron
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this case, we show a reduction from local distributed approximation algorithms for the vertex cover problem to sublinear approximation algorithms for this problem.  ...  This reduction can be modified easily and applied to other optimization problems that have local distributed approximation algorithms, such as the dominating set problem.  ...  We thank Luca Trevisan for telling us about the lower bound described in Section 6, and for suggesting that we present a sketch of this lower bound in the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.04.040">doi:10.1016/j.tcs.2007.04.040</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lzbxthg43fgvfbmjixu7442oem">fatcat:lzbxthg43fgvfbmjixu7442oem</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190318125049/https://core.ac.uk/download/pdf/82698330.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/e9/5be9047df38132a69e13aadfa0167781359090f3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.04.040"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Constant-Time Approximation Algorithms via Local Improvements

Huy N. Nguyen, Krzysztof Onak
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">2008 49th Annual IEEE Symposium on Foundations of Computer Science</a> </i> &nbsp;
The running time of the algorithm is independent of n, and only depends on d and ε.  ...  The problems amenable to our technique include Vertex Cover, Maximum Matching, Maximum Weight Matching, Set Cover, and Minimum Dominating Set.  ...  Acknowledgement The authors thank Ronitt Rubinfeld for her invaluable help in improving the presentation of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/focs.2008.81">doi:10.1109/focs.2008.81</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/NguyenO08.html">dblp:conf/focs/NguyenO08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/44tusnvm4vbzvbzuw5yplne7r4">fatcat:44tusnvm4vbzvbzuw5yplne7r4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808182109/https://onak.pl/download/publications/Nguyen_Onak-constant_time_approximation.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9c/ae/9caea8b49997b1f285588361e458f6b2d9e3df37.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/focs.2008.81"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Sublinear-Time Algorithms for Approximating Graph Parameters [chapter]

Dana Ron
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Similar results hold for the size of a minimum dominating set and maximum independent set. Maximum Matching.  ...  Hence, we need to design more efficient algorithms, that is, algorithms that run in sublinear time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-91908-9_7">doi:10.1007/978-3-319-91908-9_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kmecif47t5a73opeipxehp64yu">fatcat:kmecif47t5a73opeipxehp64yu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200510110409/https://link.springer.com/content/pdf/10.1007%2F978-3-319-91908-9_7.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/73/60/7360e8d47ef7dbe9d88cd641d2516410fcac3e50.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-91908-9_7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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