منابع مشابه
Planar Graph Perfect Matching is in NC
Is perfect matching in NC? That is to say, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC matching algorithms. Within this question, the case of planar graphs has remained an enigma: On the one hand, counting the number of perfect matchings is far harder t...
متن کاملPlanar Perfect Matching is in NC
Consider a planar graph G = (V,E) with polynomially bounded edge weight function w : E → [0, poly(n)]. The main results of this paper are NC algorithms for the following problems: • minimum weight perfect matching in G, • maximum cardinality and maximum weight matching in G when G is bipartite, • maximum multiple-source multiple-sink flow in G where c : E → [1, poly(n)] is a polynomially bounde...
متن کاملThe Polynomially Bounded Perfect Matching Problem Is in NC 2
The perfect matching problem is known to be in ¶, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite ...
متن کاملPerfect Matching in Bipartite Planar Graphs is in UL
We prove that Perfect Matching in bipartite planar graphs is in UL, improving upon the previous bound of SPL (see [DKR10]) on its space complexity. We also exhibit space complexity bounds for some related problems. Summarizing, we show that, constructing: 1. a Perfect Matching in bipartite planar graphs is in UL 2. a Hall Obstacle in bipartite planar graphs is in NL; 3. an Even Perfect Matching...
متن کاملNearly-Perfect Hypergraph Packing is in NC
Answering a question of RR odl and Thoma, we show that the Nibble Algorithm for nding a collection of disjoint edges covering almost all vertices in an almost regular, uniform hypergraph with negligible pair degrees can be derandomized and parallelized to run in polylog time on polynomially many parallel processors. In other words, the nearly-perfect packing problem on this class of hypergraphs...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2020
ISSN: 0004-5411,1557-735X
DOI: 10.1145/3397504