Introduction to algorithms
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Finding critical independent sets and critical vertex subsets are polynomial problems
SIAM Journal on Discrete Mathematics
On Finding Critical Independent and Vertex Sets
SIAM Journal on Discrete Mathematics
Improved Algorithms for Bipartite Network Flow
SIAM Journal on Computing
Bipartite graphs and their applications
Bipartite graphs and their applications
A combinatorial algorithm for weighted stable sets in bipartite graphs
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Communication: Minimum cost homomorphisms to semicomplete multipartite digraphs
Discrete Applied Mathematics
Minimum Cost Homomorphism Dichotomy for Locally In-Semicomplete Digraphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Introduction to the Maximum Solution Problem
Complexity of Constraints
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
New Plain-Exponential Time Classes for Graph Homomorphism
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
The complexity of soft constraint satisfaction
Artificial Intelligence
Minimum cost homomorphisms to oriented cycles with some loops
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
On the approximation of minimum cost homomorphism to bipartite graphs
Discrete Applied Mathematics
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Level of repair analysis (LORA) is a prescribed procedure for defense logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize overall life-cycle costs. For a LORA problem with two levels of indenture with three possible repair decisions, which is of interest in UK and US military and which we call LORA-BR, Barros [The optimisation of repair decisions using life-cycle cost parameters. IMA J. Management Math. 9 (1998) 403-413] and Barros and Riley [A combinatorial approach to level of repair analysis, European J. Oper. Res. 129 (2001) 242-251] developed certain branch-and-bound heuristics. The surprising result of this paper is that LORA-BR is, in fact, polynomial-time solvable. To obtain this result, we formulate the general LORA problem as an optimization homomorphism problem on bipartite graphs, and reduce a generalization of LORA-BR, LORA-M, to the maximum weight independent set problem on a bipartite graph. We prove that the general LORA problem is NP-hard by using an important result on list homomorphisms of graphs. We introduce the minimum cost graph homomorphism problem, provide partial results and pose an open problem. Finally, we show that our result for LORA-BR can be applied to prove that an extension of the maximum weight independent set problem on bipartite graphs is polynomial time solvable.