• Management Science and Financial Engineering
• /
• v.15 no.1
• /
• pp.71-79
• /
• 2009

This paper considers the two kinds of integer multicommodity flow problems, a feasibility problem and a maximization problem, on two types of directed cycles, a unidirectional and a bidirectional cycle. Both multicommodity flow problems on an undirected cycle have been dealt with by many researchers and it is known that each problems can be solved by a polynomial time algorithm. However, we don't find any result on the directed cycles. Here we show that we can also solve both problems for a unidirectional and a bidirectional cycle in polynomial time.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.05a
• /
• pp.1025-1029
• /
• 2006

This paper considers the multicommodity flow problem and the integer multicommodity flow problem on cycle graphs. We present two linear time algorithms for solving each of the two problems.

• Management Science and Financial Engineering
• /
• v.16 no.3
• /
• pp.85-93
• /
• 2010

Given an undirected network with a set of source-sink pairs, we are assumed to get a benefit if a pair of source and sink nodes are connected. The k-edge survivability of a network is defined as the total benefit secured after arbitrarily selected k edges are destroyed. The problem of computing k-edge survivability is known to be NP-hard and has applications of evaluating the survivability or vulnerability of a network. In this paper, we consider the k-edge survivability problem restricted to ring networks and develop an algorithm to solve it in O($n^3$|K|) time where n is the number of nodes and K is the set of source-sink pairs.