Abstract
The fastest known algorithms for many problems on graphs use matrix multiplication as a sub-routine. Some examples of problems solved using matrix multiplication are recognition of transitive graphs, computing the transitive closure of a directed acyclic graph, and finding the neighborhood containment matrix of a graph. In this paper, we show how to avoid using matrix multiplication for these problems on special classes of graphs. This leads to efficient algorithms for recognizing chordal comparability graphs and trapezoid graphs, computing the transitive closure of two dimensional partial orders, and a number of other problems.KeywordsPartial OrderTransitive ClosureInterval GraphChordal GraphInterval OrderThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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