A faster distributed algorithm for computing maximal matchings deterministically

We show that maximal matchings can be computed deterministically in O(log4 n) rounds in the synchronous, message-passing model of computation. This improves on an earlier result by three log-factors.

[1]  Michael Luby.  Removing Randomness in Parallel Computation without a Processor Penalty , 1993, J. Comput. Syst. Sci..

[2]  Moni Naor,et al.  A Lower Bound on Probabilistic Algorithms for Distributive Ring Coloring , 1991, SIAM J. Discret. Math..

[3]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[4]  Andrew V. Goldberg,et al.  Parallel symmetry-breaking in sparse graphs , 1987, STOC.

[5]  Richard M. Karp,et al.  Probabilistic recurrence relations , 1994, JACM.

[6]  Alessandro Panconesi,et al.  On the distributed complexity of computing maximal matchings , 1997, SODA '98.

[7]  Shay Kutten,et al.  Fast distributed construction of k-dominating sets and applications , 1995, PODC '95.

[8]  Nathan Linial,et al.  Locality in Distributed Graph Algorithms , 1992, SIAM J. Comput..

[9]  Alessandro Panconesi,et al.  Nearly optimal distributed edge coloring in O (log log n ) rounds , 1997 .

[10]  Aravind Srinivasan,et al.  The local nature of Δ-coloring and its algorithmic applications , 1995, Comb..

[11]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[12]  Béla Bollobás.  Chromatic number, girth and maximal degree , 1978, Discret. Math..

[13]  Andrew V. Goldberg,et al.  Network decomposition and locality in distributed computation , 1989, 30th Annual Symposium on Foundations of Computer Science.

[14]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[15]  Richard Cole,et al.  Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking , 2018, Inf. Control..

[16]  Alessandro Panconesi,et al.  Nearly optimal distributed edge colouring in O(log log n) rounds , 1997, SODA '97.

[17]  Lenore Cowen,et al.  Fast network decomposition , 1992, PODC '92.

[18]  Aravind Srinivasan,et al.  On the Complexity of Distributed Network Decomposition , 1996, J. Algorithms.

[19]  N Linial,et al.  Low diameter graph decompositions , 1993, Comb..

[20]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[21]  Bela Bollobas,et al.  Graph theory , 1979 .

[22]  David B. Shmoys,et al.  Efficient Parallel Algorithms for Edge Coloring Problems , 1987, J. Algorithms.

[23]  Amos Israeli,et al.  An Improved Parallel Algorithm for Maximal Matching , 1986, Inf. Process. Lett..