Roof duality for polynomial 0-1 optimization
Mathematical Programming: Series A and B
The Boolean quadric polytope: some characteristics, facets and relatives
Mathematical Programming: Series A and B
A bound on the roof-duality gap
COMO '86 Lectures given at the third session of the Centro Internazionale Matematico Estivo (C.I.M.E.) on Combinatorial optimization
On the equivalence of paved-duality and standard linearization of nonlinear 0–1 optimization
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
Chva´tal cuts and odd cycle inequalities in quadratic 0–1 optimization
SIAM Journal on Discrete Mathematics
Persistency in quadratic 0–1 optimization
Mathematical Programming: Series A and B
Combinatorial algorithms for Boolean and pseudo-Boolean functions
Combinatorial algorithms for Boolean and pseudo-Boolean functions
Discrete Applied Mathematics
Design and performance of parallel and distributed approximation algorithms for Maxcut
Journal of Parallel and Distributed Computing
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Adaptive Memory Tabu Search for Binary Quadratic Programs
Management Science
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Discrete Applied Mathematics
Exact MAX-2SAT solution via lift-and-project closure
Operations Research Letters
The max-cut problem on graphs not contractible to K5
Operations Research Letters
Elementary closures for integer programs
Operations Research Letters
Discrete Applied Mathematics
Global optimality conditions and optimization methods for quadratic integer programming problems
Journal of Global Optimization
A study of memetic search with multi-parent combination for UBQP
EvoCOP'10 Proceedings of the 10th European conference on Evolutionary Computation in Combinatorial Optimization
A multilevel algorithm for large unconstrained binary quadratic optimization
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Discrete Applied Mathematics
Approximate MRF inference using bounded treewidth subgraphs
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Generalized roof duality for multi-label optimization: optimal lower bounds and persistency
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Tighter relaxations for higher-order models based on generalized roof duality
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Backbone guided tabu search for solving the UBQP problem
Journal of Heuristics
Probabilistic GRASP-Tabu Search algorithms for the UBQP problem
Computers and Operations Research
A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming
Applied Soft Computing
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The ''roof dual'' of a QUBO (Quadratic Unconstrained Binary Optimization) problem has been introduced in [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0-1 optimization, Mathematical Programming 28 (1984) 121-155]; it provides a bound to the optimum value, along with a polynomial test of the sharpness of this bound, and (due to a ''persistency'' result) it also determines the values of some of the variables at the optimum. In this paper we provide a graph-theoretic approach to provide bounds, which includes as a special case the roof dual bound, and show that these bounds can be computed in O(n^3) time by using network flow techniques. We also obtain a decomposition theorem for quadratic pseudo-Boolean functions, improving the persistency result of [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0-1 optimization, Mathematical Programming 28 (1984) 121-155]. Finally, we show that the proposed bounds (including roof duality) can be applied in an iterated way to obtain significantly better bounds. Computational experiments on problems up to thousands of variables are presented.