A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
Scaling Algorithms for the Shortest Paths Problem
SIAM Journal on Computing
Tractable constraints on ordered domains
Artificial Intelligence
Computability and complexity theory
Computability and complexity theory
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction to Algorithms
Formal Verification of a Combination Decision Procedure
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Higher-Order and Symbolic Computation
The Mailman algorithm: A note on matrix--vector multiplication
Information Processing Letters
A Combinatorial Algorithm for Horn Programs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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In this paper, we detail a new algorithm for the problem of checking linear and integer feasibility of a system of Horn constraints. For certain special cases, the new algorithm is faster than the "Lifting Algorithm" described in [1]. Moreover, the new approach is based on different ideas and in fact exploits several properties of Horn constraint systems (HCS) which are not known to be part of the literature. In the case of constraints of bounded width (corresponding to "loosely coupled" systems), our algorithm can be modified to run in O(n3+mċn+ mċn2/log(max(m,n))) time. Our main result establishes that checking the feasibility of an HCS can be reduced to three subproblems: negative-cost cycle detection in networks (NCCD), matrix-vector multiplication (MV), and the conversion of an HCS to a non-redundant set of difference constraints (H2D). The MV and NCCD problems have been extremely well-studied, and specialized, fast algorithms exist for relevant special cases. We have identified a new problem, H2D, which warrants future research, since improved algorithms for H2D could be implemented in our algorithm to decrease the running time.