Two NP-Complete Augmentation Problems
Two NP-Complete Augmentation Problems
Matroid partitioning.
Arc-disjoint in-trees in directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Rooted k-connections in digraphs
Discrete Applied Mathematics
Approximations for minimum and min-max vehicle routing problems
Journal of Algorithms
Operations Research Letters
| Hi-index | 0.00 |
Given a directed graph D=(V,A) with a set of d specified vertices S={s 1,驴,s d }驴V and a function f : S驴驴 where 驴 denotes the set of positive integers, we consider the problem which asks whether there exist 驴 i=1 d f(s i ) in-trees denoted by $T_{i,1},T_{i,2},\ldots,T_{i,f(s_{i})}$ for every i=1,驴,d such that $T_{i,1},\ldots,T_{i,f(s_{i})}$ are rooted at s i , each T i,j spans vertices from which s i is reachable and the union of all arc sets of T i,j for i=1,驴,d and j=1,驴,f(s i ) covers A. In this paper, we prove that such set of in-trees covering A can be found by using an algorithm for the weighted matroid intersection problem in time bounded by a polynomial in 驴 i=1 d f(s i ) and the size of D. Furthermore, for the case where D is acyclic, we present another characterization of the existence of in-trees covering A, and then we prove that in-trees covering A can be computed more efficiently than the general case by finding maximum matchings in a series of bipartite graphs.