(Almost) Tight bounds and existence theorems for single-commodity confluent flows

A flow of a commodity is said to be confluent if at any node all the flow of the commodity leaves along a single edge. In this paper we study single-commodity confluent flow problems, where we need to route given node demands to a single destination using a confluent flow. Single- and multi-commodity confluent flows arise in a variety of application areas, most notably in networking; in fact, most flows in the Internet are (multi-commodity) confluent flows since Internet routing is destination based. We present near-tight approximation algorithms, hardness results, and existence theorems for minimizing congestion in single-commodity confluent flows. The maximum edge congestion of a single-commodity confluent flow occurs at one of the incoming edges of the destination. Therefore, finding a minimum-congestion confluent flow is equivalent to the following problem: given a directed graph G with k sinks and non-negative demands on all the nodes of G, determine a confluent flow th...

• Type: Journal
• Year: 2007
• Where: JACM
• Authors: Jiangzhuo Chen, Robert D. Kleinberg, László Lovász, Rajmohan Rajaraman, Ravi Sundaram, Adrian Vetta
• Keywords: Confluent, Confluent flow, JACM 2007, Single-commodity Confluent flow