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arXiv · cs/0205042

Orienting Graphs to Optimize Reachability

S. L. Hakimi·E. Schmeichel·Neal E. Young
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Abstract

The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to minimize the number of such pairs. The paper describes a quadratic-time algorithm for the first problem, and a proof that the second problem is NP-hard to approximate within some constant 1+epsilon > 1. The latter proof also shows that the second problem is equivalent to ``comparability graph completion''; neither problem was previously known to be NP-hard.

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S. L. Hakimi, E. Schmeichel, Neal E. Young. 2002-05-18. Orienting Graphs to Optimize Reachability. https://doi.org/10.1016/s0020-0190(97)00129-4

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