Graph Partitioning and Traffic Grooming with Bounded Degree Request Graph

Abstract

We study a graph partitioning problem which arises from traffic grooming in optical networks. We wish to minimize the equipment cost in a SONET WDM ring network by minimizing the number of Add-Drop Multiplexers (ADMs) used. We consider the version introduced by Muñoz and Sau [12] where the ring is unidirectional with a grooming factor C, and we must design the network (namely, place the ADMs at the nodes) so that it can support any request graph with maximum degree at most Δ. This problem is essentially equivalent to finding the least integer M(C,Δ) such that the edges of any graph with maximum degree at most Δ can be partitioned into subgraphs with at most C edges and each vertex appears in at most M(C,Δ) subgraphs [12]. The cases where Δ= 2 and Δ = 3,C ≠ 4 were solved by Muñoz and Sau [12]. In this article we establish the value of M(C,Δ) for many more cases, leaving open only the case where Δ ≥ 5 is odd, $\Delta \pmod{2C}$ is between 3 and C − 1, C ≥ 4, and the request graph does not contain a perfect matching. In particular, we answer a conjecture of [12].

This work has been partially supported by: 1st author: NSERC; 2nd author: European project IST FET AEOLUS, PACA region of France, Ministerio de Ciencia e Innovación, European Regional Development Fund under project MTM2008-06620-C03-01/MTM, and Catalan Research Council under project 2005SGR00256.