Determining graph properties from matrix representations
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A Survey of Analysis Techniques for Discrete Algorithms
ACM Computing Surveys (CSUR)
Reference machines require non-linear time to maintain disjoint sets
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
On the complexity of the Maximum Subgraph Problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees
IEEE Transactions on Computers
Testing whether a digraph contains H-free k-induced subgraphs
Theoretical Computer Science
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We investigate the maximum number C(P) of arguments of P that must be tested in order to compute P, a Boolean function of d Boolean arguments. We present evidence for the general conjecture that C(P)&equil;d whenever P(0d) @@@@ P(1d) and P is left invariant by a transitive permutation group acting on the arguments. A non-constructive argument (not based on the construction of an “oracle”) proves the generalized conjecture for d a prime power. We use this result to prove the Aanderaa-Rosenberg conjecture by showing that at least v2/9 entries of the adjacency matrix of a v-vertex undirected graph G must be examined in the worst case to determine if G has any given non-trivial monotone graph property.