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Hardness of Low Delay Network Scheduling

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3 Author(s)
Shah, D. ; Lab. of Inf. & Decision Syst. (LIDS), Massachusetts Inst. of Technol., Cambridge, MA, USA ; Tse, D.N.C. ; Tsitsiklis, J.N.

We consider a communication network and study the problem of designing a high-throughput and low-delay scheduling policy that only requires a polynomial amount of computation at each time step. The well-known maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas' randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints and (b) the standard SINR (signal to interference noise ratio) model. We show that unless NPBPP (or P = NP for the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network's capacity, there does not exist a low-delay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas' randomized algorithm must grow super-polynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994).

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Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 12 )