Improved Deterministic Distributed Matching via Rounding

We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is a deterministic distributed rounding method for certain linear programs, which is the first such rounding method, to our knowledge. A sampling of our end results is as follows: • AnO ( log ∆ logn ) -round deterministic distributed algorithm for computing a maximal matching, in n-node graphs with maximum degree ∆. This is the first improvement in about 20 years over the celebrated O(log n)-round algorithm of Hanckowiak, Karonski, and Panconesi [SODA’98, PODC’99]. • AnO ( log ∆ log 1 ε + log∗ n ) -round deterministic distributed algorithm for a (2+ε)-approximation of maximum matching. This is exponentially faster than the classic O(∆ + log∗ n)-round 2approximation of Panconesi and Rizzi [DIST’01]. With some modifications, the algorithm can also find an almost maximal matching which leaves only an ε-fraction of the edges on unmatched nodes. • An O ( log ∆ log 1 ε log1+ε W + log ∗ n ) -round deterministic distributed algorithm for a (2+ ε)approximation of a maximum weighted matching, and also for the more general problem of maximum weighted b-matching. Here, W denotes the maximum normalized weight. These improve over the O ( log n log1+ε W ) -round (6+ε)-approximation algorithm of Panconesi and Sozio [DIST’10].