It is well known that the generalized max-weight matching (GMWM) scheduling policy, and in general throughput-optimal scheduling policies, often require the solution of a complex optimization problem, making their implementation prohibitively difficult in practice. This has motivated many researchers to develop distributed sub-optimal algorithms that approximate the GMWM policy. One major assumption commonly shared in this context is that the time required to find an appropriate schedule vector is negligible compared to the length of a timeslot. This assumption may not be accurate as the time to find schedule vectors usually increases polynomially with the network size. On the other hand, we intuitively expect that for many sub-optimal algorithms, the schedule vector found becomes a better estimate of the one returned by the GMWM policy as more time is given to the algorithm. We thus, in this paper, consider the problem of scheduling from a new perspective through which we carefully incorporate channel variations and time-efficiency of sub-optimal algorithms into the scheduler design. Specifically, we propose a dynamic control policy (DCP) that works on top of a given sub-optimal algorithm, and dynamically but in a large time-scale adjusts the time given to the algorithm according to queue backlog and channel correlations. This policy does not require the knowledge of the structure of the given sub-optimal algorithm, and with low-overhead can be implemented in a distributed manner. Using a novel Lyapunov analysis, we characterize the stability region induced by DCP, and show that our characterization can be tight. We also show that the stability region of DCP is at least as large as the one for any other static policy. Finally, we provide two case studies to gain further intuition into the performance of DCP.
The closest work to ours in this paper is @cite_29 , where based on the linear-complexity algorithm in @cite_31 , the impact of channel memory on the stability region of a general class of sub-optimal algorithms is studied. Despite its consideration for channel variations, this work still does not model the search-time, and implicitly assumes it is negligible.
@cite_29 @cite_31
2140867429 2963922654 2086179657 1555149635
We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed by their outer product wx*. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that, for “generic” signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L. That is, we show that if x is drawn from a random subspace of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length N, which we code using a random L x N coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length K, then the receiver can recover both the channel response and the message when L ≳ N + K, to within constant and log factors. In this paper, a diffusion-based molecular communication channel between two nano-machines is considered. The effect of the amount of memory on performance is characterized, and a simple memory-limited decoder is proposed; its performance is shown to be close to that of the best possible decoder (without any restrictions on the computational complexity or its functional form), using genie-aided upper bounds. This effect is adapted to the case of Molecular Concentration Shift Keying; it is shown that a four-bit memory achieves nearly the same performance as infinite memory for all of the examples considered. A general class of threshold decoders is considered and shown to be suboptimal for a Poisson channel with memory, unless the SNR is higher than a computed threshold. During each symbol duration (symbol period), the probability that a released molecule hits the receiver changes over the duration of the period; thus, we also consider a receiver that samples at a rate higher than the transmission rate (a multi-read system). A multi-read system improves performance. The associated decision rule for this system is shown to be a weighted sum of the samples during each symbol interval. The performance of the system is analyzed using the saddle point approximation. The best performance gains are achieved for an oversampling factor of three for the examples considered. Abstract We propose a novel approach to solving the approximate k-nearest neighbor search problem in metric spaces. The search structure is based on a navigable small world graph with vertices corresponding to the stored elements, edges to links between them, and a variation of greedy algorithm for searching. The navigable small world is created simply by keeping old Delaunay graph approximation links produced at the start of construction. The approach is very universal, defined in terms of arbitrary metric spaces and at the same time it is very simple. The algorithm handles insertions in the same way as queries: by finding approximate neighbors for the inserted element and connecting it to them. Both search and insertion can be done in parallel requiring only local information from the structure. The structure can be made distributed. The accuracy of the probabilistic k-nearest neighbor queries can be adjusted without rebuilding the structure. The performed simulation for data in the Euclidean spaces shows that the structure built using the proposed algorithm has small world navigation properties with log 2 ( n ) insertion and search complexity at fixed accuracy, and performs well at high dimensionality. Simulation on a CoPHiR dataset revealed its high efficiency in case of large datasets (more than an order of magnitude less metric computations at fixed recall) compared to permutation indexes. Only 0.03 of the 10 million 208-dimensional vector dataset is needed to be evaluated to achieve 0.999 recall (virtually exact search). For recall 0.93 processing speed 2800 queries s can be achieved on a dual Intel X5675 Xenon server node with Java implementation. This paper presents essentially optimal lower bounds on the size of linear codes C : 0, 1 n ? 0, 1 m which have the property that, for constants ?, ? > 0, any bit of the message can be recovered with probability 1 2 + ? by an algorithm reading only 2 bits of a codeword corrupted in up to ?m positions. Such codes are known to be applicable to, among other things, the construction and analysis of information-theoretically secure private information retrieval schemes. In this work, we show that m must be at least 2?(? 1-2? n). Our results extend work by Goldreich, Karloff, Schulman, and Trevisan [GKST02], which is based heavily on methods developed by Katz and Trevisan [KT00]. The key to our improved bounds is an analysis which bypasses an intermediate reduction used in both prior works. The resulting improvement in the efficiency of the overall analysis is sufficient to achieve a lower bound optimal within a constant factor in the exponent. A construction of a locally decodable linear code matching this bound is presented.