Journal of Combinatorial Theory Series B
A High Girth Graph Construction
SIAM Journal on Discrete Mathematics
Approximating the traffic grooming problem in tree and star networks
Journal of Parallel and Distributed Computing
Approximating the traffic grooming problem
Journal of Discrete Algorithms
Hardness and approximation of traffic grooming
Theoretical Computer Science
Graph Partitioning and Traffic Grooming with Bounded Degree Request Graph
Graph-Theoretic Concepts in Computer Science
Traffic grooming in WDM networks
IEEE Communications Magazine
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
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We study the following graph partitioning problem: Given two positive integers $C$ and $\Delta$, find the least integer $M(C,\Delta)$ such that the edges of any graph with maximum degree at most $\Delta$ can be partitioned into subgraphs with at most $C$ edges and each vertex appears in at most $M(C,\Delta)$ subgraphs. This problem is naturally motivated by traffic grooming, which is a major issue in optical networks. Namely, we introduce a new pseudodynamic model of traffic grooming in unidirectional rings, in which the aim is to design a network able to support any request graph with a given bounded degree. We show that optimizing the equipment cost under this model is essentially equivalent to determining the parameter $M(C,\Delta)$. We establish the value of $M(C,\Delta)$ for almost all values of $C$ and $\Delta$, leaving open only the case where $\Delta \geq 5$ is odd, $\Delta \pmod{2C}$ is between $3$ and $C-1$, $C\geq 4$, and the request graph does not contain a perfect matching. For these open cases, we provide upper bounds that differ from the optimal value by at most one.