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Constraint graph
About: Constraint graph is a research topic. Over the lifetime, 1608 publications have been published within this topic receiving 35446 citations.
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TL;DR: A new hypergraph-partitioning algorithm that is based on the multilevel paradigm, which scales very well for large hypergraphs and produces high-quality partitioning in a relatively small amount of time.
Abstract: In this paper, we present a new hypergraph-partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraph-partitioning algorithm produces high-quality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%-23% better than those produced by other state-of-the-art schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring 4-10 times less time than that required by the other schemes. Our multilevel hypergraph-partitioning algorithm scales very well for large hypergraphs. Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today's workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9%-30%).
941 citations
13 Jun 1997
TL;DR: The experiments show that the multilevel hypergraph partitioning algorithm produces high quality partitioning in relatively small amount of time and outperforms other schemes (in hyperedge cut) quite consistently with larger margins.
Abstract: In this paper, we present a new hypergraph partitioning algorithmthat is based on the multilevel paradigm. In the multilevel paradigm,a sequence of successively coarser hypergraphs is constructed. Abisection of the smallest hypergraph is computed and it is used toobtain a bisection of the original hypergraph by successively projectingand refining the bisection to the next level finer hypergraph.We evaluate the performance both in terms of the size of the hyper-edgecut on the bisection as well as run time on a number of VLSIcircuits. Our experiments show that our multilevel hypergraph partitioningalgorithm produces high quality partitioning in relativelysmall amount of time. The quality of the partitionings produced byour scheme are on the average 4% to 23% better than those producedby other state-of-the-art schemes. Furthermore, our partitioning algorithmissignificantly faster, often requiring 4 to 15 times less timethan that required by the other schemes. Our multilevel hypergraphpartitioning algorithm scales very well for large hypergraphs. Hypergraphswith over 100,000 vertices can be bisected in a few minuteson today's workstations. Also, on the large hypergraphs, ourscheme outperforms other schemes (in hyperedge cut) quite consistentlywith larger margins (9% to 30%).
887 citations
TL;DR: It is shown how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can beused also in newly defined schemes.
Abstract: We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (+ and X) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.
709 citations
TL;DR: An integrated strategy is described which utilizes the distinct advantages of each scheme and shows that, in hard problems, the average improvement realized by the integrated scheme is 20–25% higher than any of the individual schemes.
553 citations
01 Jun 1988
TL;DR: This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally by generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs.
Abstract: Many AI tasks can be formulated as Constraint-Satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.
552 citations