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P versus NP and other resource-bounded computation.

17 votes
2 answers
699 views

H-free cut problem

Suppose you are given a connected, simple, undirected graph H. The H-free cut problem is defined as follows: Given a simple, undirected graph G, is there a cut (partition of vertices into two …
11 votes
1 answer
332 views

Minimum weight subforest of given cardinality

This question was motivated by a question asked on stackoverflow. Suppose you are given a rooted tree $T$ (i.e. there is a root and nodes have children etc) on $n$ nodes (labelled $1, 2, \dots, n$). …
12 votes
Accepted

Reducing complexity with parallelism

If you mean O(1) processors, then no, computation complexity cannot be reduced. Simply line up the work done by each processor and do it on a single one. If you are worried about synchronization, the …
Aryabhata's user avatar
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31 votes
2 answers
2k views

Hierarchies in NP (under the assumption that P != NP)

Assuming that P != NP, I believe it has been shown that there are problems which are not in P and not NP-Complete. Graph Isomorphism is conjectured to be such a problem. Is there any evidence of more …