Pradipta Mitra

Nearly optimal bounds for distributed wireless scheduling in the SINR model

We study the wireless scheduling problem in the physically realistic SINR model. More specifically: we are given a set of n links, each a sender-receiver pair. We would like to schedule the links using the minimum number of slots, using the SINR model of interference among simultaneously transmitting links. In the basic problem, all senders transmit with the same uniform power. In this work, we provide a distributed O(log n)-approximation for the scheduling problem, matching the best ratio known for centralized algorithms. This is based on an algorithm studied by Kesselheim and Vocking, improving their analysis by a logarithmic factor. We show this to be best possible for any such distributed algorithm. Our analysis extends also to linear power assignments, and as well as for more general assignments, modulo assumptions about message acknowledgement mechanisms.

On a game theoretic approach to capacity maximization in wireless networks

We consider the capacity problem (or, the single slot scheduling problem) in wireless networks. Our goal is to maximize the number of successful connections in arbitrary wirelessnetworks where a transmission is successful only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. We study a game theoretic approach towards capacity maximization introduced by Andrews and Dinitz (INFOCOM 2009) and Dinitz (INFOCOM 2010). We prove vastly improved bounds for the game theoretic algorithm. In doing so, we achieve the first distributed constant factor approximation algorithm for capacity maximization for the uniform power assignment. When compared to the optimum where links may use an arbitrary power assignment, we prove a O(log Δ) approximation, where Δ is the ratio between the largest and the smallest link in the network. This is an exponential improvement of the approximation factor compared to existing results for distributed algorithms. All our results work for links located in any metric space. In addition, we provide simulation studies clarifying the picture on distributed algorithms for capacity maximization.

Towards tight bounds for local broadcasting

We consider the local broadcasting problem in the SINR model, which is a basic primitive for gathering initial information among n wireless nodes. Assuming that nodes can measure received power, we achieve an essentially optimal constant approximate algorithm (with a log2 n additive term). This improves upon the previous best O(log n)-approximate algorithm. Without power measurement, our algorithm achieves O(log n)-approximation, matching the previous best result, but with a simpler approach that works under harsher conditions, such as arbitrary node failures. We give complementary lower bounds under reasonable assumptions.

Wireless capacity and admission control in cognitive radio

We give algorithms with constant-factor performance guarantees for several capacity and throughput problems in the SINR model. The algorithms are all based on a novel LP formulation for capacity problems. First, we give a new constant-factor approximation algorithm for selecting the maximum subset of links that can be scheduled simultaneously, under any non-decreasing and sublinear power assignment. For the case of uniform power, we extend this to the case of variable QoS requirements and link-dependent noise terms. Second, we approximate a problem related to cognitive radio: find a maximum set of links that can be simultaneously scheduled without affecting a given set of previously assigned links. Finally, we obtain constant-factor approximation of weighted capacity under linear power assignment.

Distributed connectivity of wireless networks

We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set of n points in the plane, and b) scheduling it efficiently in the SINR model of interference. The nodes must converge on a solution in a distributed manner, having no means of communication beyond the sole wireless channel. We give distributed connectivity algorithms that run in time O(poly(log δ, log n)), where δ is the ratio between the longest and shortest distances among nodes. Given that algorithm without prior knowledge of the instance are essentially limited to using uniform power, this is close to best possible. Our primary aim, however, is to find efficient structures, measured in the number of slots used in the final schedule of the links. Our main result is algorithms that match the efficiency of centralized solutions. Specifically, the networks can be scheduled in O(log n) slots using (arbitrary) power control, and in O(log n (log log δ + log n)) slots using a simple oblivious power scheme. Additionally, the networks have the desirable properties that the latency of a converge-cast and of any node-to-node communication is optimal O(log n) time.

A fully distributed algorithm for throughput performance in wireless networks

We study link scheduling in wireless networks under stochastic arrival processes of packets, and give an algorithm that achieves stability in the physical (SINR) interference model. The efficiency of such an algorithm is the fraction of the maximum feasible traffic that the algorithm can handle without queues growing indefinitely. Our algorithm achieves two important goals: (i) efficiency is independent of the size of the network, and (ii) the algorithm is fully distributed, i.e., individual nodes need no information about the overall network topology, not even local information.

Connectivity and aggregation in multihop wireless networks

We present randomized distributed algorithms for connectivity and aggregation in multi-hop wireless networks under the SINR model. The connectivity problem asks for a set of links that strongly connect a given set of wireless nodes, along with an efficient schedule. Aggregation asks for a spanning in-arborescence (converge-cast tree), along with a schedule that additionally obeys the partial order defined by the tree. Here we treat the multi-hop case, where nodes have limited power that restricts the links they can potentially form. We show that connectivity is possible for any set of n nodes in O(\log n) slots, which matches the best centralized bound known, and that aggregation is possible in O(D + log n) time (D being the maximum hop-distance), which is optimal.

Wireless network stability in the SINR model

We study the stability of wireless networks under stochastic arrival processes of packets, and design efficient, distributed algorithms that achieve stability in the SINR (Signal to Interference and Noise Ratio) interference model. Specifically, we make the following contributions. We give a distributed algorithm that achieves

Wireless capacity with arbitrary gain matrix

\Omega(\frac{1}{\log^2 n})

Maximum MIMO Flow in wireless networks under the SINR model

-efficiency on all networks (where n is the number of links in the network), for all length monotone, sub-linear power assignments. For the power control version of the problem, we give a distributed algorithm with