Journal ArticleDOI
The quadratic minimum spanning tree problem
Arjang A. Assad,Weixuan Xu +1 more
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In this article, the authors introduced a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure, which is proven to be NP-hard.Abstract:
This article introduces a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure This quadratic minimum spanning tree problem is proven to be NP-hard A technique for generating lower bounds for this problem is discussed and incorporated into branch-and-bound schemes for obtaining exact solutions Two heuristic algorithms are also developed Computational experience with both exact and heuristic algorithms is reportedread more
Citations
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Journal ArticleDOI
Genetic algorithm approach on multi-criteria minimum spanning tree problem
Gengui Zhou,Mitsuo Gen +1 more
TL;DR: The proposed method adopts the Prufer number as the tree encoding and applies the Multiple Criteria Decision Making (MCDM) technique and nondominated sorting technique to make the GA search give out all Pareto optimal solutions.
Book ChapterDOI
An AIS-ACO Hybrid Approach for Multi-Objective Distribution System Reconfiguration
A. Ahuja,Sanjoy Das,Anil Pahwa +2 more
TL;DR: A hybrid algorithm based on artificial immune systems and ant colony optimization for distribution system reconfiguration, which is formulated as a multi-objective optimization problem, and the use of the pheromones to obtain quick solutions to restore the distribution system under contingency situations is proposed.
Proceedings ArticleDOI
Approximating submodular functions everywhere
TL;DR: In this article, the problem of finding a monotone, submodular function f on a ground set of size n, after only poly(n) oracle queries was considered.
Journal Article
Approximating Submodular Functions Everywhere
TL;DR: The problem of approximating a non-negative, monotone, submodular function f on a ground set of size n everywhere is considered, after only poly(n) oracle queries, and it is shown that no algorithm can achieve a factor better than Ω(√n/log n), even for rank functions of a matroid.
Journal ArticleDOI
A swarm intelligence approach to the quadratic minimum spanning tree problem
Shyam Sundar,Alok Singh +1 more
TL;DR: An artificial bee colony (ABC) algorithm is presented, a new swarm intelligence approach inspired by intelligent foraging behavior of honey bees, to solve the quadratic minimum spanning tree problem.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
TL;DR: Kurosh and Levitzki as discussed by the authors, on the radical of a general ring and three problems concerning nil rings, Bull Amer Math Soc vol 49 (1943) pp 913-919 10 -, On the structure of algebraic algebras and related rings.
Journal ArticleDOI
Shortest connection networks and some generalizations
TL;DR: In this paper, the basic problem of interconnecting a given set of terminals with a shortest possible network of direct links is considered, and a set of simple and practical procedures are given for solving this problem both graphically and computationally.