A (2 + ∊)-Approximation for Maximum Weight Matching in the Semi-Streaming Model

We present a simple deterministic single-pass (2 + ϵ)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves upon the currently best known approximation ratio of (3.5 + ϵ). Our algorithm uses O(n log2 n) space for constant values of ϵ. It relies on a variation of the local-ratio theorem, which may be of independent interest in the semi-streaming model.

[1]  Christian Konrad,et al.  Maximum Matching in Turnstile Streams , 2015, ESA.

[2]  Silvio Lattanzi,et al.  Filtering: a method for solving graph problems in MapReduce , 2011, SPAA '11.

[3]  Sofya Vorotnikova,et al.  Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams , 2016, SODA.

[4]  Sanjeev Khanna,et al.  Approximating matching size from random streams , 2014, SODA.

[5]  Ashwinkumar Badanidiyuru,et al.  Buyback Problem - Approximate Matroid Intersection with Cancellation Costs , 2010, ICALP.

[6]  Mariano Zelke,et al.  Weighted Matching in the Semi-Streaming Model , 2007, Algorithmica.

[7]  Reuven Bar-Yehuda,et al.  A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem , 1983, WG.

[8]  Leah Epstein,et al.  Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model , 2009, SIAM J. Discret. Math..

[9]  Joan Feigenbaum,et al.  On graph problems in a semi-streaming model , 2005, Theor. Comput. Sci..

[10]  Amit Chakrabarti,et al.  Submodular maximization meets streaming: matchings, matroids, and more , 2013, Math. Program..

[11]  Yang Li,et al.  Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model , 2016, SODA.

[12]  Ami Paz,et al.  A (2+ε)-Approximation for Maximum Weight Matching in the Semi-streaming Model , 2019, ACM Trans. Algorithms.

[13]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[14]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2000, STOC '00.

[15]  Michael Crouch,et al.  Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching , 2014, APPROX-RANDOM.

[16]  Ashish Goel,et al.  On the communication and streaming complexity of maximum bipartite matching , 2012, SODA.

[17]  Silvio Micali,et al.  An O(v|v| c |E|) algoithm for finding maximum matching in general graphs , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[18]  Andrew McGregor,et al.  Finding Graph Matchings in Data Streams , 2005, APPROX-RANDOM.

[19]  Dror Rawitz,et al.  Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004 , 2004, CSUR.

[20]  Samson Zhou,et al.  Streaming Weighted Matchings: Optimal Meets Greedy , 2016, ArXiv.

[21]  Andrew McGregor,et al.  Dynamic Graphs in the Sliding-Window Model , 2013, ESA.

[22]  Chris Schwiegelshohn,et al.  Sublinear Estimation of Weighted Matchings in Dynamic Data Streams , 2015, ESA.

[23]  Yang Li,et al.  On Estimating Maximum Matching Size in Graph Streams , 2017, SODA.

[24]  Mikhail Kapralov,et al.  Better bounds for matchings in the streaming model , 2012, SODA.