Greedy algorithm and symmetric matroids
Mathematical Programming: Series A and B
Directed submodularity, ditroids and directed submodular flows
Mathematical Programming: Series A and B
Discrete Mathematics
On totally dual integral systems
Discrete Applied Mathematics
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
Delta-Matroids, Jump Systems, and Bisubmodular Polyhedra
SIAM Journal on Discrete Mathematics
A characterization of bisubmodular functions
Discrete Mathematics
On structures of bisubmodular polyhedra
Mathematical Programming: Series A and B
The membership problem in jump systems
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Minimization of an M-convex function
Discrete Applied Mathematics
Polynomial-Time Algorithms for Linear and Convex Optimization on Jump Systems
SIAM Journal on Discrete Mathematics
Even factors, jump systems, and discrete convexity
Journal of Combinatorial Theory Series B
Neighbor Systems and the Greedy Algorithm
SIAM Journal on Discrete Mathematics
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The concept of neighbor system, introduced by Hartvigsen in 2010, is a set of integral vectors satisfying a certain combinatorial property. In this paper, we reveal the relationship of neighbor systems with jump systems and with bisubmodular polyhedra. We first prove that for every neighbor system, there exists a jump system which has the same neighborhood structure as the original neighbor system. This shows that the concept of neighbor system is essentially equivalent to that of jump system. We next show that the convex closure of a neighbor system is an integral bisubmodular polyhedron. In addition, we give a characterization of neighbor systems using bisubmodular polyhedra. Finally, we consider the problem of minimizing a separable convex function on a neighbor system. It is shown that the problem can be solved in weakly polynomial time for a class of neighbor systems.