An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding

Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem . We formulate the problem as a discrete linear pr...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 32; no. 4; pp. 1017 - 1035
Main Authors: Wu, Chenchen, Xu, Dachuan, Du, Donglei, Xu, Wenqing
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2016
Springer Nature B.V
Subjects:
Algorithms
Approximation
Bivariate analysis
Circuit design
Combinatorial analysis
Combinatorics
Complex variables
Convex and Discrete Geometry
Integrated circuits
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Partitions (mathematics)
Rounding
Semidefinite programming
Theory of Computation
Complex semidefinite programming
Approximation algorithm
Balanced Max-3-Uncut
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem . We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-015-9880-z