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: An -round deterministic distributed algorithm for computing a maximal matching, in -node graphs with maximum degree . This is the first improvement in about 20 years over the celebrated -round algorithm of Hanckowiak, Karonski, and Panconesi [SODA'98, PODC'99]. nA deterministic distributed algorithm for computing a -approximation of maximum matching in rounds. This is exponentially faster than the classic -round 2-approximation of Panconesi and Rizzi [DIST'01]. With some modifications, the algorithm can also find an almost maximal matching which leaves only an -fraction of the edges on unmatched nodes. An -round deterministic distributed algorithm for computing a -approximation of a maximum weighted matching, and also for the more general problem of maximum weighted -matching. Here, denotes the maximum normalized weight. These improve over the -round -approximation algorithm of Panconesi and Sozio [DIST'10].