핵심 개념
An efficient polynomial-time algorithm for enumerating all extreme points of a bisubmodular polyhedron.
초록
The content presents an efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron. The key highlights are:
- The algorithm uses the reverse search technique proposed by Avis and Fukuda to avoid redundant searches.
- It leverages the characterization of the adjacency of extreme points using signed posets, as developed by Ando and Fujishige.
- The algorithm has a time complexity of O(n^4|V|) and a space complexity of O(n^2), where n is the dimension of the underlying space and |V| is the number of extreme points.
- The algorithm also has an O(n^6) time delay, meaning the time between two consecutive outputs is bounded by a polynomial function of the input size.
- The capacity functions required in the algorithm can be computed efficiently in constant time, without the need to solve bisubmodular function minimization problems.
- The algorithm is a generalization of the enumeration algorithm for base polyhedra, which encompasses various combinatorial enumeration problems.
- The algorithm has potential applications in machine learning and artificial intelligence, where bisubmodular functions are used to model deep multivariate submodular functions.