Generalization of Min-Cut Partitioning to Tree Structures and its Applications
IEEE Transactions on Computers
Approximation and Intractability Results for the Maximum Cut Problem and Its Variants
IEEE Transactions on Computers
On the approximation of maximum satisfiability
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Detailed layer assignment for MCM routing
ICCAD '92 1992 IEEE/ACM international conference proceedings on Computer-aided design
Layer assignment for high-performance multi-chip modules
ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
P-Complete Approximation Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
New Approximation Results on Graph Matching and related Problems
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Conjugate conflict continuation graphs for multi-layer constrained via minimization
Information Sciences: an International Journal
Exploiting hierarchy and structure to efficiently solve graph coloring as SAT
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
On greedy construction heuristics for the MAX-CUT problem
International Journal of Computational Science and Engineering
Accelerating large graph algorithms on the GPU using CUDA
HiPC'07 Proceedings of the 14th international conference on High performance computing
Overlaying multiple maps efficiently
CIT'04 Proceedings of the 7th international conference on Intelligent Information Technology
Stitch-aware routing for multiple e-beam lithography
Proceedings of the 50th Annual Design Automation Conference
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There are a number of VLSI problems that have a common structure. We investigate such a structure that leads to a unified approach for three independent VLSI layout problems: partitioning, placement, and via minimization. Along the line, we first propose a linear-time approximation algorithm on maxcut and two closely related problems: k-coloring and maximal k-color ordering problem. The k-coloring is a generalization of the maxcut and the maximal k-color ordering is a generalization of the k-coloring. For a graph G with e edges and n vertices, our maxcut approximation algorithm runs in O(e + n) sequential time yielding a node-balanced maxcut with size at least (w(E) + w(E)/n)/2, improving the time complexity of O(e log e) known before. Building on the proposed maxcut technique and employing a height-balanced binary decomposition, we devise an O((e + n)log k) time algorithm for the k-coloring problem which always finds a k-partition of vertices such that the number of bad (or "defected") edges does not exceed (w(E)/k)((n$-$ 1)/n)log k, thus improving both the time complexity O(enk) and the bound e/k known before. The other related problem is the maximal k-color ordering problem that has been an open problem [16]. We show the problem is NP-complete, then present an approximation algorithm building on our k-coloring structure. A performance bound on maximal k-color ordering cost, 2kw(E)/3 is attained in O(ek) time. The solution quality of this algorithm is also tested experimentally and found to be effective.