Theory of linear and integer programming
Theory of linear and integer programming
Submodular functions in graph theory
Discrete Mathematics
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality
Mathematical Programming: Series A and B
Block-Triangularizations of Partitioned Matrices under Similarity/Equivalence Transformations
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
A dichotomy theorem for maximum generalized satisfiability problems
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A capacity scaling algorithm for convex cost submodular flows
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
A Faster Scaling Algorithm for Minimizing Submodular Functions
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Approximability of Three-valued MAX CSP
SIAM Journal on Computing
Submodular function minimization
Mathematical Programming: Series A and B
SIAM Journal on Discrete Mathematics
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
A Faster Strongly Polynomial Time Algorithm for Submodular Function Minimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
The complexity of soft constraint satisfaction
Artificial Intelligence
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Towards minimizing k-submodular functions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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Let (L;@?,@?) be a finite lattice and let n be a positive integer. A function f:L^n-R is said to be submodular if f(a@?b)+f(a@?b)@?f(a)+f(b) for all a,b@?L^n. In this article we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding x@?L^n such that f(x)=min"y"@?"L"^"nf(y) as efficiently as possible. We establish *a min-max theorem, which states that the minimum of the submodular function is equal to the maximum of a certain function defined over a certain polyhedron; and *a good characterisation of the minimisation problem, i.e., we show that given an oracle for computing a submodular f:L^n-Z and an integer m such that min"x"@?"L"^"nf(x)=m, there is a proof of this fact which can be verified in time polynomial in n and max"t"@?"L"^"nlog|f(t)|; and *a pseudopolynomial-time algorithm for the minimisation problem, i.e., given an oracle for computing a submodular f:L^n-Z one can find min"t"@?"L"^"nf(t) in time bounded by a polynomial in n and max"t"@?"L"^"n|f(t)|.