2017/03/02 by Fischer, Manuela · 3 citations
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1703.00900
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 O(log2 Δ⋅ log n)-round deterministic distributed algorithm for computing a maximal matching, in n-node graphs with maximum degree Δ. This is the first improvement in about 20 years over the celebrated O(log4 n)-round algorithm of Hańćkowiak, Karoński, and Panconesi [SODA'98, PODC'99]. -- A deterministic distributed algorithm for computing a (2+ε)-approximation of maximum matching in O(log2 Δ⋅ log (1)/(ε) + log^ * n) rounds. This is exponentially faster than the classic O(Δ+log^* n)-round 2-approximation of Panconesi and Rizzi [DIST'01]. With some modifications, the algorithm can also find an ε-maximal matching which leaves only an ε-fraction of the edges on unmatched nodes. -- An O(log2 Δ⋅ log (1)/(ε) + log^ * n)-round deterministic distributed algorithm for computing a (2+ε)-approximation of a maximum weighted matching, and also for the more general problem of maximum weighted b-matching. These improve over the O(log4 n ⋅ log1+ε W)-round (6+ε)-approximation algorithm of Panconesi and Sozio [DIST'10], where W denotes the maximum normalized weight.