Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
A capacity improvement lower bound for fixed charge network design problems
Operations Research
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
Graph Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Online multicast routing with bandwidth guarantees: a new approach using multicast network flow
IEEE/ACM Transactions on Networking (TON)
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
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We introduce the following network optimization problem: given a directed graph with a cost function on the arcs, demands at the nodes, and a single source s, find the minimum cost connected subgraph from s such that its total demand is no less than lower bound D. We describe applications of this problem to disaster relief and media broadcasting, and show that it generalizes several well-known models including the knapsack problem, the partially ordered knapsack problem, the minimum branching problem, and certain scheduling problems. We prove that our problem is strongly NP-complete and give an integer programming formulation. We also provide five heuristic approaches, illustrate them with a numerical example, and provide a computational study on both small and large sized, randomly generated problems. The heuristics run efficiently on the tested problems and provide solutions that, on average, are fairly close to optimal.