A faster algorithm for finding the minimum cut in a graph
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Near-optimal nonapproximability results for some NPO PB-complete problems
Information Processing Letters
Reload cost problems: minimum diameter spanning tree
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
Note: The complexity of a minimum reload cost diameter problem
Discrete Applied Mathematics
The Minimum Reload s-t Path/Trail/Walk Problems
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Speeding up IP-based algorithms for constrained quadratic 0–1 optimization
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
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We are given a digraph G = (N,A), where each arc is colored with one among k given colors. We look for a spanning arborescence T of G rooted (wlog) at node 1 and having minimum changeover cost. We call this the Minimum Changeover Cost Arborescence problem. To the authors' knowledge, it is a new problem. The concept of changeover costs is similar to the one, already considered in the literature, of reload costs, but the latter depend also on the amount of commodity flowing in the arcs and through the nodes, whereas this is not the case for the changeover costs. Here, given any node j ≠1, if a is the color of the single arc entering node j in arborescence T, and b is the color of an arc (if any) leaving node j, then these two arcs contribute to the total changeover cost of T by the quantity dab, an entry of a k-dimensional square matrix D. We first prove that our problem is NPO-complete and very hard to approximate. Then we present Integer Programming formulations together with a combinatorial lower bound, a greedy heuristic and an exact solution approach. Finally, we report extensive computational results and exhibit a set of challenging instances.