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- W1941062520 abstract "We present two methods for finding a lowest common ancestor (LCA) for each pair of vertices of a directed acyclic graph (dag) on n vertices and m edges. The first method is surprisingly natural and solves the all-pairs LCA problem for the input dag on n vertices and m edges in time O(nm). As a corollary, we obtain an O(n 2)-time algorithm for finding genealogical distances considerably improving the previously known O(n 2.575) time-bound for this problem. The second method relies on a novel reduction of the all-pairs LCA problem to the problem of finding maximum witnesses for Boolean matrix product. We solve the latter problem and hence also the all-pairs LCA problem in time $O(n^{{2}+frac{1}{4-omega}})$ , where ω =2.376 is the exponent of the fastest known matrix multiplication algorithm. This improves the previously known $O(n^{frac{omega+3}{2}})$ time-bound for the general all-pairs LCA problem in dags." @default.
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- W1941062520 date "2005-01-01" @default.
- W1941062520 modified "2023-09-26" @default.
- W1941062520 title "LCA Queries in Directed Acyclic Graphs" @default.
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- W1941062520 doi "https://doi.org/10.1007/11523468_20" @default.
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