A (k + 1)-approximation Robust network flow algorithm and a tighter heuristic method using iterative multiroute flow

Abstract

We consider two variants of a max-flow problem against k edge failures, each of which can be both approximated by a multiroute flow algorithm. The maximum k-robust flow problem is to find the minimum max-flow value among networks that can be obtained by deleting each set of k edges. The maximum k-balanced flow problem is to find a max-flow of the network such that the flow value is maximum against any set of k edge failures, when deleting the corresponding flow to those k edges in the original flow. We prove, where C M is the max-(k + 1)-route flow value, C M′ is the effectiveness of the max-(k + 1)-route flow after k attacks, C B is the max-k-balanced flow value, and C R is the max-k-robust flow value. Also, we develop a polynomial-time heuristic algorithm for both cases, called the iterative multiroute flow. Our experimental results show that the average improvement made by our heuristic method can be up to 10% better than the multiroute flow algorithm. Compared to the optimal max-k-robust flow solutions-obtained by a brute-force algorithm-there is an average gap of 2% at most. © 2014 Springer International Publishing Switzerland.