By Topic

Fast approximation algorithms on maxcut, k-coloring, and k-color ordering for VLSI applications

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Jun-dong Cho ; Dept. of Electron. Eng., Sung Kyun Kwan Univ., Suwon, South Korea ; Raje, S. ; Sarrafzadeh, M.

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 nodebalanced 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. 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

Published in:

Computers, IEEE Transactions on  (Volume:47 ,  Issue: 11 )