On packing and coloring hyperedges in a cycle
Discrete Applied Mathematics
Wavelength management in WDM rings to maximize the number of connections
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
The price of anarchy for selfish ring routing is two
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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In the demand routing and slotting problem on unit demands (unit-DRSP), we are given a set of unit demands on an n-node ring. Each demand, which is a (source, destination) pair, 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 deterministic approximation algorithm guarantees a solution that is 2 × OPT. A demand of unit-DRSP can be viewed as a chord on the ring. Let w denote the size of the largest set of demand chords that mutually cross in the interior of the ring. We present a simple approximation algorithm that uses at most $(2 - 1/\lceil w/2 \rceil)\times OPT$ slots in an n-node network; this is the first deterministic approximation algorithm that beats the factor of 2 for all values of OPT and therefore for all instances of the input. If randomization is allowed, an algorithm by Kumar produces, with high probability, a solution that uses asymptotically $(1.5 + \frac{1}{2e} +o(1)) \times OPT$ slots. However, when OPT is not large enough, the factor can exceed 2. In this paper, we show how combining our algorithm with Kumar's yields a randomized approximation algorithm that has, with high probability, a constant factor of $2 - 1/\theta(\log n)$. While asymptotically it is not better than Kumar's, the approximation factor holds for all values of OPT.