A lower bound for the recognition of digraph properties

Abstract

The complexity of a digraph property is the number of entries of the adjacency matrix which must be examined by a decision tree algorithm to recognize the property in the worst case, Aanderaa and Rosenberg conjectured that there is a constantε such that every digraph property which is monotone (not destroyed by the deletion of edges) and nontrivial (holds for some but not all digraphs) has complexity at leastεv 2 wherev is the number of nodes in the digraph. This conjecture was proved by Rivest and Vuillemin and a lower bound ofv 2/4−o(v 2) was subsequently found by Kahn, Saks, and Sturtevant. Here we show a lower bound ofv 2/2−o(v 2). We also prove that a certain class of monotone, nontrivial bipartite digraph properties is evasive (requires that every entry in the adjacency matrix be examined in the worst case).

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King, V. A lower bound for the recognition of digraph properties. Combinatorica 10, 53–59 (1990). https://doi.org/10.1007/BF02122695

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AMS subject classifications (1980)

  • 05C20
  • 05C35
  • 05C99