Theory of linear and integer programming
Theory of linear and integer programming
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
A Zero-Space algorithm for Negative Cost Cycle Detection in networks
Journal of Discrete Algorithms
A new algorithm for linear and integer feasibility in horn constraints
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
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In this paper, we design and analyze a simple, greedy algorithm for a class of linear programs called Horn programs. This algorithm, which we term as the "Lifting Algorithm", is a variant of the Stressing Algorithm proposed for Difference Constraint systems in [5] and runs in time O(m·n 2) on a Horn system with m constraints and n variables. Inasmuch as Horn constraints subsume difference constraints, and all known algorithms for the problem of checking feasibility in Difference Constraint Systems run in time 驴(m·n), the running time of our algorithm is only a factor n worse than the best known running time for checking feasibility in Difference Constraint Systems. Horn programs arise in a number of application areas including econometrics and program verification; consequently, their study is well-motivated. An important feature of our algorithm is that it uses only one operator, viz., addition. We also show that our algorithm can identify the linear and lattice point feasibility of Extended Horn Systems in O(m ·n 2) time.