Distributed Fractional Local Ratio and Independent Set Approximation
Pages 281 - 299
Abstract
We consider the Maximum Weight Independent Set problem, with a focus on obtaining good approximations for graphs of small maximum degree . We give deterministic local algorithms running in time that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below , and a further improvement to when .
Technically, this is achieved by leveraging the fractional local ratio technique, for a first application in a distributed setting.
References
[1]
Alon N Goldreich O On constant time approximation of parameters of bounded degree graphs Property Testing 2010 Heidelberg Springer 234-239
[2]
Bar-Noy A, Bar-Yehuda R, Freund A, Naor J, and Schieber B A unified approach to approximating resource allocation and scheduling JACM 2001 48 5 1069-1090
[3]
Bar-Yehuda R, Bendel K, Freund A, and Rawitz D Local ratio: a unified framework for approximation algorithms in memoriam: Shimon Even 1935–2004 ACM Comput. Surv. 2004 36 4 422-463
[4]
Bar-Yehuda, R., Censor-Hillel, K., Ghaffari, M., Schwartzman, G.: Distributed approximation of maximum independent set and maximum matching. In: 36th PODC, pp. 165–174 (2017)
[5]
Bar-Yehuda, R., Censor-Hillel, K., Schwartzman, G.: A distributed -approximation for vertex cover in rounds. JACM 64(3), 23:1–23:11 (2017)
[6]
Bar-Yehuda R and Even S A local-ratio theorem for approximating the weighted vertex cover problem Ann. Discret. Math. 1985 25 27-46
[7]
Bar-Yehuda R, Halldórsson MM, Naor J, Shachnai H, and Shapira I Scheduling split intervals SIAM J. Comput. 2006 36 1 1-15
[8]
Bar-Yehuda R and Rawitz D Using fractional primal-dual to schedule split intervals with demands Discret. Optim. 2006 3 4 275-287
[9]
Barenboim, L.: Deterministic ( + 1)-coloring in sublinear (in ) time in static, dynamic, and faulty networks. JACM 63(5), 47:1–47:22 (2016)
[10]
Barenboim L, Elkin M, and Kuhn F Distributed ( + 1)-coloring in linear () time SIAM J. Comput. 2014 43 1 72-95
[11]
Ben-Basat R, Even G, Kawarabayashi K, and Schwartzman G Lotker Z and Patt-Shamir B A deterministic distributed 2-approximation for weighted vertex cover in rounds Structural Information and Communication Complexity 2018 Cham Springer 226-236
[12]
Bodlaender, M.H., Halldórsson, M.M., Konrad, C., Kuhn, F.: Brief announcement: local independent set approximation. In: PODC, pp. 377–378. ACM (2016)
[13]
Boppana RB, Halldórsson MM, and Rawitz D Simple and local independent set approximation Theoret. Comput. Sci. 2020 846 27-37
[14]
Canzar S, Elbassioni KM, Klau GW, and Mestre J On tree-constrained matchings and generalizations Algorithmica 2015 71 1 98-119
[15]
Censor-Hillel, K., Khoury, S., Paz, A.: Quadratic and near-quadratic lower bounds for the CONGEST model. In: 31st DISC, pp. 10:1–10:16 (2017)
[16]
Chan SO Approximation resistance from pairwise-independent subgroups JACM 2016 63 3 27
[17]
Faour, S., Ghaffari, M., Grunau, C., Kuhn, F., Rozhon, V.: Local distributed rounding: generalized to MIS, matching, set cover, and beyond. In: 34th SODA (2023)
[18]
Ghaffari, M., Kuhn, F., Maus, Y.: On the complexity of local distributed graph problems. In: 49th STOC, pp. 784–797 (2017)
[19]
Halldórsson MM Approximations of weighted independent set and hereditary subset problems Graph Algorithms Appl. 2004 2 3-18
[20]
Halperin E Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs SIAM J. Comput. 2002 31 5 1608-1623
[21]
Hermelin D and Rawitz D Optimization problems in multiple subtree graphs Disc. Appl. Math. 2011 159 7 588-594
[22]
Hochbaum DS Efficient bounds for the stable set, vertex cover and set packing problems Discret. Appl. Math. 1983 6 3 243-254
[23]
Kawarabayashi, K., Khoury, S., Schild, A., Schwartzman, G.: Improved distributed approximations for maximum independent set. In: 34th DISC, LIPIcs, vol. 179, pp. 35:1–35:16 (2020)
[24]
Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: 17th SODA, pp. 980–989 (2006)
[25]
Kuhn, F., Moscibroda, T., Wattenhofer, R.: Local computation: Lower and upper bounds. JACM 63(2), 17:1–17:44 (2016)
[26]
Lewin-Eytan L, Naor J, and Orda A Admission control in networks with advance reservations Algorithmica 2004 40 4 293-304
[27]
Maus, Y., Peltonen, S., Uitto, J.: Distributed symmetry breaking on power graphs via sparsification. In: 42nd PODC, pp. 157–167 (2023)
[28]
Patt-Shamir B, Rawitz D, and Scalosub G Distributed approximation of cellular coverage J. Parallel Distrib. Comput. 2012 72 3 402-408
[29]
Rawitz D Admission control with advance reservations in simple networks J. Discret. Algorithms 2007 5 3 491-500
[30]
Rawitz, D.: Local ratio. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics. Methologies and Traditional Applications, 2nd edn, vol. 1, pp. 87–111. Chapman and Hall/CRC (2018)
Recommendations
Local ratio method on partial set multi-cover
In this paper, we study the minimum partial set multi-cover problem (PSMC). Given an element set E, a collection of subsets $${\mathcal {S}}\subseteq 2^E$$S⊆2E, a cost $$c_S$$cS on each set $$S\in {\mathcal {S}}$$SźS, a covering requirement $$r_e$$re ...
An improved distributed algorithm for maximal independent set
SODA '16: Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithmsThe Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents a very simple randomized algorithm for this problem providing a near-optimal local complexity, which ...
Distributed maximal independent set using small messages
SODA '19: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete AlgorithmsMaximal Independent Set (MIS) is one of the central problems in distributed graph algorithms. The celebrated works of Luby [STOC'85] and Alon, Babai, and Itai [JALG'86] provide O(log n)-round randomized distributed MIS algorithms, which work with O(log ...
Comments
Information & Contributors
Information
Published In
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 27 May 2024
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 11 Feb 2025