Faster Network Algorithms Based on Graph Decomposition

We propose faster algorithms for the maximum flow problem and related problems based on graph decomposition. Our algorithms first construct indices (data structures) from a given graph, then use them for solving the problems. A basic problem is an all pairs maximum flow problem, which consists of two stages. In a preprocessing stage we construct an index, and in a query stage we process the query using the index. We can solve all pairs maximum flow problem and minimum cut problem using the indices. Time complexities of our algorithms depend on the size of the maximum triconnected component in the graph, say r. Our algorithms run faster than known algorithms if r is small. The maximum flow problem can be solved in O(nr) time, which is faster than the best known O(nm) algorithm [Orlin 2013] if r = o(m), where n and m are the numbers of vertices and edges, respectively.