Abstract
The demand routing and slotting problem on unit demands (unit-DRSP) arises from constructing a SONET ring to minimize cost. Given a set of unit demands on an n-node ring, each demand must be routed clockwise or counterclockwise and assigned a slot so that no two routes that overlap occupy the same slot. The objective is to minimize the total number of slots used.
It is well known that unit-DRSP is NP-complete. The best approximation algorithm guarantees a solution to within twice of optimality. In the special case when the optimal solution uses many colors, a recent algorithm by Kumar [12] beats the approximation factor of 2. A demand of unit-DRSP can be viewed as a chord on the ring whose endpoints correspond to the source and destination of the demand. Let w denote the size of the largest set of demand chords that pairwise intersect in the interior of the ring. We first present an algorithm that achieves an approximation factor of 2–2/(w+1) in an n-node network. We then show how to combine our algorithm with Kumar’s to achieve a hybrid algorithm with an an approximation factor of (2–max{4/n,1/(50log n)}).
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Cheng, C.T. (1999). A New Approximation Algorithm for the Demand Routing and Slotting Problem with Unit Demands on Rings. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 1999 1999. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48413-4_22
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DOI: https://doi.org/10.1007/978-3-540-48413-4_22
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