arXiv subjects

Chandramani Singh

Publications and source records attributed to Chandramani Singh.

25 records · Page 2Linked to original sources

arXiv2018

Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learning

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known randomized online coordinate descent algorithms. Furthermore, the proposed algorithms for stochastic optimization exhibit as good convergence rates as the best known randomized coordinate descent algorithms. We also show simulation results to demonstrate performance of the proposed algorithms.

cs.LG↗

arXiv2013

Analysis of a Proportionally Fair and Locally Adaptive spatial Aloha in Poisson Networks

The proportionally fair sharing of the capacity of a Poisson network using Spatial-Aloha leads to closed-form performance expressions in two extreme cases: (1) the case without topology information, where the analysis boils down to a parametric optimization problem leveraging stochastic geometry; (2) the case with full network topology information, which was recently solved using shot-noise techniques. We show that there exists a continuum of adaptive controls between these two extremes, based on local stopping sets, which can also be analyzed in closed form. We also show that these control schemes are implementable, in contrast to the full information case which is not. As local information increases, the performance levels of these schemes are shown to get arbitrarily close to those of the full information scheme. The analytical results are combined with discrete event simulation to provide a detailed evaluation of the performance of this class of medium access controls.

cs.NI↗

arXiv2013

Adaptive Spatial Aloha, Fairness and Stochastic Geometry

This work aims at combining adaptive protocol design, utility maximization and stochastic geometry. We focus on a spatial adaptation of Aloha within the framework of ad hoc networks. We consider quasi-static networks in which mobiles learn the local topology and incorporate this information to adapt their medium access probability (MAP) selection to their local environment. We consider the cases where nodes cooperate in a distributed way to maximize the global throughput or to achieve either proportional fair or max-min fair medium access. In the proportional fair case, we show that nodes can compute their optimal MAPs as solutions to certain fixed point equations. In the maximum throughput case, the optimal MAPs are obtained through a Gibbs Sampling based algorithm. In the max min case, these are obtained as the solution of a convex optimization problem. The main performance analysis result of the paper is that this type of distributed adaptation can be analyzed using stochastic geometry in the proportional fair case. In this case, we show that, when the nodes form a homogeneous Poisson point process in the Euclidean plane, the distribution of the optimal MAP can be obtained from that of a certain shot noise process w.r.t. the node Poisson point process and that the mean utility can also be derived from this distribution. We discuss the difficulties to be faced for analyzing the performance of the other cases (maximum throughput and max-min fairness). Numerical results illustrate our findings and quantify the gains brought by spatial adaptation in such networks.

cs.NI↗

arXiv2012

Neighbor Oblivious and Finite-State Algorithms for Circumventing Local Minima in Geographic Forwarding

We propose distributed link reversal algorithms to circumvent communication voids in geographic routing. We also solve the attendant problem of integer overflow in these algorithms. These are achieved in two steps. First, we derive partial and full link reversal algorithms that do not require one-hop neighbor information, and convert a destination-disoriented directed acyclic graph (DAG) to a destination-oriented DAG. We embed these algorithms in the framework of Gafni and Bertsekas ("Distributed algorithms for generating loop-free routes in networks with frequently changing topology", 1981) in order to establish their termination properties. We also analyze certain key properties exhibited by our neighbor oblivious link reversal algorithms, e.g., for any two neighbors, their t-states are always consecutive integers, and for any node, its t-state size is upper bounded by log(N). In the second step, we resolve the integer overflow problem by analytically deriving one-bit full link reversal and two-bit partial link reversal versions of our neighbor oblivious link reversal algorithms.

cs.NI↗

arXiv2011

Combined Base Station Association and Power Control in Multi-channel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

cs.NI↗

arXiv2011

Optimal Forwarding in Delay Tolerant Networks with Multiple Destinations

We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.

cs.NI↗

arXiv2011

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals who can connect to the base station that offers the best utility. The signal to interference and noise ratio is used as the quantity that determines the association. We first study the SINR association-game: we determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: (i) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; (ii) A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: we determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

cs.NI↗