NDLI: Negative thinking by incremental problem solving: application to unate covering

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Negative thinking by incremental problem solving: application to unate covering

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Timing analysis and optimization (tutorial): from devices to systems

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Design technology for building wireless systems (tutorial)

Negative thinking by incremental problem solving: application to unate covering

Content Provider	ACM Digital Library
Author	Villa, Tiziano Goldberg, Evguenii I. Carloni, Luca P. Sangiovanni-Vincentelli, Alberto L. Brayton, Robert K.
Abstract	We introduce a new technique to solve exactly a discrete optimization problem, based on the paradigm of "negative" thinking. The motivation is that when searching the space of solutions, often a good solution is reached quickly and then improved only a few times before the optimum is found: hence most of the solution space is explored to certify optimality, but it does not yield any improvement of the cost function. So it is quite natural for an algorithm to be "skeptical" about the chance to improve the current best solution. For illustration we have applied our approach to the unate covering problem. We designed a procedure, raiser, implementing a negative thinking search, which is incorporated into a common branch-and-bound procedure. Raiser is invoked at a node of the search tree which is deep enough to justify negative thinking. Raiser tries to detect a hard core of the matrix corresponding to the node by augmenting an independent set of rows in order to increase incrementally the cost of the minimum solutions covering the matrix. Eventually either raiser prunes the subtree rooted at the node (having found a lower bound equal or greater than the current best solution) or returns a new solution that becomes the current best one. Experiments show that our program, aura, outperforms both espresso and our enhancement of espresso using Coudert's limit lower bound. It is always faster and in the most difficult examples either has a running time better by up to two orders of magnitude, or the other programs fail to finish due to timeout or spaceout. The package scherzo is faster on some examples and loses on others, due to a less powerful pruning strategy of the search space, partially mitigated by a more effective computation of the maximal independent set.
Starting Page	91
Ending Page	98
Page Count	8
File Format	PDF
ISBN	0818682000
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1997-11-13
Access Restriction	Subscribed
Subject Keyword	Negative thinking covering problem discrete optimization
Content Type	Text
Resource Type	Article

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