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Integration, the VLSI Journal
Partitioning similarity graphs: a framework for declustering problems
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Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
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Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Web Mining: Information and Pattern Discovery on the World Wide Web
ICTAI '97 Proceedings of the 9th International Conference on Tools with Artificial Intelligence
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STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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This article presents an infinite family of combinatorial problems that shows abrupt changes of complexity between neighbour problems. We define problem P"k^l as a purely constraint-driven variant of hypergraph partitioning with parameters k and l as follows. Given a hypergraph on n vertices and k sizes of colours t"1,...,t"k of sum n, can we colour the vertices with k colours of given size such that each hyperedge intersects at most l colours? We show that, for fixed parameters k and l, P"k^l is: polynomial when l=1, and NP-complete when l1 on the class of hypergraphs; NP-complete when l=1, and linear when l1 on the class of hypergraphs with pairwise disjoint hyperedges. This inversion of complexity is possible since hypergraphs with disjoint hyperedges can be encoded in a more compact way, namely @Q(mlog(n)) instead of @Q(mn) bits (n and m are the number of vertices and edges of the hypergraph).