Convexity on unions of sets
Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem
The 3-Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n≥6, the 3-Interchange Graph is a graph on 1/2(n-1)! vertices, corresponding to the hamiltonian tours in K_n; two vertices are adjacent iff the corresponding hamiltonian tours differ in an interchange of 3 edges; i.e. the tours differ in a single 3-Opt step. It is shown that the 3-Interchange Graph is a hamiltonian subgraph of the Symmetric Traveling Salesman Polytope. Upper bounds are derived...
Johann Bernoulli (1667-1748): Deset neklidných let v Groningen
On the complexity of determining tolerances for ε-optimal solutions to min-max combinatorial optimization problems
This paper studies the complexity of sensitivity analysis for optimal and ε-optimal solutions to general 0-1 combinatorial optimization problems with min-max objectives. Van Hoesel and Wagelmans [9] have studied the complexity of sensitivity analysis of optimal and ε-optimal solutions to min-sum problems, and Ramaswamy et al. [17] the complexity of sensitivity analysis of optimal solutions to min-max problems. We show that under some mild assumptions the sensitivity analysis of ε-optimal solutions...
Convex polytopes as matrix invariants
Nearly principal minors of -matrices
Starshapedness and its applications to input-output models
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