Greedy algorithm and symmetric matroids
Mathematical Programming: Series A and B
Generalized polymatroids and submodular flows
Mathematical Programming: Series A and B
Directed submodularity, ditroids and directed submodular flows
Mathematical Programming: Series A and B
Discrete Mathematics
Delta-Matroids, Jump Systems, and Bisubmodular Polyhedra
SIAM Journal on Discrete Mathematics
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
A greedy algorithm for maximizing a linear objective function
Discrete Applied Mathematics
M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem
SIAM Journal on Discrete Mathematics
Polynomial-Time Algorithms for Linear and Convex Optimization on Jump Systems
SIAM Journal on Discrete Mathematics
Neighbor Systems, Jump Systems, and Bisubmodular Polyhedra
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
A neighbor system, introduced in this paper, is a collection of integral vectors in $\mathbb{R}^{n}$ with some special structure. Such collections (slightly) generalize jump systems, which, in turn, generalize integral bisubmodular polyhedra, integral polymatroids, delta-matroids, matroids, and other structures. We show that neighbor systems provide a systematic and simple way to characterize these structures. One of our main results is a simple greedy algorithm for optimizing over (finite) neighbor systems starting from any feasible vector. The algorithm is (essentially) identical to the usual greedy algorithm on matroids and integral polymatroids when the starting vector is zero. But in all other cases, from matroids through jump systems, it appears to be a new greedy algorithm. We end the paper by introducing another structure, which is more general than neighbor systems, and indicate that essentially the same greedy algorithm also works for this structure.