Handling irregular ILP within conventional VLIW schedulers using artificial resource constraints
CASES '00 Proceedings of the 2000 international conference on Compilers, architecture, and synthesis for embedded systems
Enumerating all connected maximal common subgraphs in two graphs
Theoretical Computer Science
Efficiently covering complex networks with cliques of similar vertices
Theoretical Computer Science - Complex networks
An algorithm for reporting maximal c-cliques
Theoretical Computer Science
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Invitation to data reduction and problem kernelization
ACM SIGACT News
Algorithms for compact letter displays: Comparison and evaluation
Computational Statistics & Data Analysis
A backtracking search tool for constructing combinatorial test suites
Journal of Systems and Software
Data reduction and exact algorithms for clique cover
Journal of Experimental Algorithmics (JEA)
Note: A note on the problem of reporting maximal cliques
Theoretical Computer Science
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The search for minimum clique coverings of graphs appears in many practical guises and with several possible minimization goals. One reasonable goal is to minimize the number of overall cliques in a covering, while a second less well-studied but equally reasonable goal is to minimize the number of individual assignments of vertices to cliques. Both goals constitute NP-hard problems and as such require competitive algorithms for practical progress to be made toward their resolutions. In this article, we introduce a technique for accomplishing the latter goal, using a combination of data reduction and a backtracking algorithm. In addition, we demonstrate that it is not always possible to minimize both the number of cliques and the number of individual vertex-clique assignments simultaneously. This demonstration resolves an open question and underscores the need for techniques that specifically minimize the number of assignments of vertices to cliques. We then illustrate our approach in two practical examples. We follow these examples with a simulation-based comparison of our exact approach with a heuristic based on the state-of-the-art algorithm for minimizing the number of cliques in a clique covering. For this comparison, we consider graphs likely to arise in applied statistics, a category of applications for which minimizing individual vertex-clique assignments is of particular interest.