A constant factor approximation algorithm for boxicity of circular arc graphs

The boxicity (resp. cubicity) of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (resp. cubes) in R-k. Equivalently, it is the minimum number of interval graphs (resp. unit interval graphs) on the vertex set V, such that the intersection of their edge sets is E. The problem of computing boxicity (resp. cubicity) is known to be inapproximable, even for restricted graph classes like bipartite, co-bipartite and split graphs, within an O(n(1-epsilon))-factor for any epsilon > 0 in polynomial time, unless NP = ZPP. For any well known graph class of unbounded boxicity, there is no known approximation algorithm that gives n(1-epsilon)-factor approximation algorithm for computing boxicity in polynomial time, for any epsilon > 0. In this paper, we consider the problem of approximating the boxicity (cubicity) of circular arc graphs intersection graphs of arcs of a circle. Circular arc graphs are known to have unbounded boxicity, which could be as large as Omega(n). We give a (2 + 1/k) -factor (resp. (2 + log n]/k)-factor) polynomial time approximation algorithm for computing the boxicity (resp. cubicity) of any circular arc graph, where k >= 1 is the value of the optimum solution. For normal circular arc (NCA) graphs, with an NCA model given, this can be improved to an additive two approximation algorithm. The time complexity of the algorithms to approximately compute the boxicity (resp. cubicity) is O(mn + n(2)) in both these cases, and in O(mn + kn(2)) = O(n(3)) time we also get their corresponding box (resp. cube) representations, where n is the number of vertices of the graph and m is its number of edges. Our additive two approximation algorithm directly works for any proper circular arc graph, since their NCA models can be computed in polynomial time. (C) 2014 Elsevier B.V. All rights reserved.

A Modified Sum-Product Algorithm over Graphs with Isolated Short Cycles

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

A Distributed TDMA Slot Scheduling Algorithm for Spatially Correlated Contention in WSNs

In WSNs the communication traffic is often time and space correlated, where multiple nodes in a proximity start transmitting simultaneously. Such a situation is known as spatially correlated contention. The random access method to resolve such contention suffers from high collision rate, whereas the traditional distributed TDMA scheduling techniques primarily try to improve the network capacity by reducing the schedule length. Usually, the situation of spatially correlated contention persists only for a short duration, and therefore generating an optimal or suboptimal schedule is not very useful. Additionally, if an algorithm takes very long time to schedule, it will not only introduce additional delay in the data transfer but also consume more energy. In this paper, we present a distributed TDMA slot scheduling (DTSS) algorithm, which considerably reduces the time required to perform scheduling, while restricting the schedule length to the maximum degree of interference graph. The DTSS algorithm supports unicast, multicast, and broadcast scheduling, simultaneously without any modification in the protocol. We have analyzed the protocol for average case performance and also simulated it using Castalia simulator to evaluate its runtime performance. Both analytical and simulation results show that our protocol is able to considerably reduce the time required for scheduling.

A provably tight delay-driven concurrently congestion mitigating global routing algorithm

Routing is a very important step in VLSI physical design. A set of nets are routed under delay and resource constraints in multi-net global routing. In this paper a delay-driven congestion-aware global routing algorithm is developed, which is a heuristic based method to solve a multi-objective NP-hard optimization problem. The proposed delay-driven Steiner tree construction method is of O(n(2) log n) complexity, where n is the number of terminal points and it provides n-approximation solution of the critical time minimization problem for a certain class of grid graphs. The existing timing-driven method (Hu and Sapatnekar, 2002) has a complexity O(n(4)) and is implemented on nets with small number of sinks. Next we propose a FPTAS Gradient algorithm for minimizing the total overflow. This is a concurrent approach considering all the nets simultaneously contrary to the existing approaches of sequential rip-up and reroute. The algorithms are implemented on ISPD98 derived benchmarks and the drastic reduction of overflow is observed. (C) 2014 Elsevier Inc. All rights reserved.

A faster algorithm for testing polynomial representability of functions over finite integer rings

Given a function from Z(n) to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over Z(n) by constructing a generating set for the Z(n)-module of polynomial functions. This characterization results in an algorithm that is faster on average in deciding polynomial representability. We also extend the characterization to functions in several variables. (C) 2015 Elsevier B.V. All rights reserved.

Energy Sharing for Multiple Sensor Nodes With Finite Buffers

We consider the problem of finding optimal energy sharing policies that maximize the network performance of a system comprising of multiple sensor nodes and a single energy harvesting (EH) source. Sensor nodes periodically sense the random field and generate data, which is stored in the corresponding data queues. The EH source harnesses energy from ambient energy sources and the generated energy is stored in an energy buffer. Sensor nodes receive energy for data transmission from the EH source. The EH source has to efficiently share the stored energy among the nodes to minimize the long-run average delay in data transmission. We formulate the problem of energy sharing between the nodes in the framework of average cost infinite-horizon Markov decision processes (MDPs). We develop efficient energy sharing algorithms, namely Q-learning algorithm with exploration mechanisms based on the epsilon-greedy method as well as upper confidence bound (UCB). We extend these algorithms by incorporating state and action space aggregation to tackle state-action space explosion in the MDP. We also develop a cross entropy based method that incorporates policy parameterization to find near optimal energy sharing policies. Through simulations, we show that our algorithms yield energy sharing policies that outperform the heuristic greedy method.

A New Successive Displacement Type Load Flow Algorithm and its Application to Radial Systems

A new successive displacement type load flow method is developed in this paper. This algorithm differs from the conventional Y-Bus based Gauss Seidel load flow in that the voltages at each bus is updated in every iteration based on the exact solution of the power balance equation at that node instead of an approximate solution used by the Gauss Seidel method. It turns out that this modified implementation translates into only a marginal improvement in convergence behaviour for obtaining load flow solutions of interconnected systems. However it is demonstrated that the new approach can be adapted with some additional refinements in order to develop an effective load flow solution technique for radial systems. Numerical results considering a number of systems-both interconnected and radial, are provided to validate the proposed approach.

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.

A New Algorithm for Nonparametric Sequential Detection

We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to a general family of distributions. We propose a simple algorithm to address the problem. Its performance is analysed and asymptotic properties are proved. The simulated and analysed performance of the algorithm is compared with an earlier algorithm addressing the same problem with similar assumptions. Finally, we provide a justification for our model motivated by a Cognitive Radio scenario and modify the algorithm for optimizing performance when information about the prior probabilities of occurrence of the two hypotheses is available.

Reduced Look Ahead Orthogonal Matching Pursuit

Compressed Sensing (CS) is an elegant technique to acquire signals and reconstruct them efficiently by solving a system of under-determined linear equations. The excitement in this field stems from the fact that we can sample at a rate way below the Nyquist rate and still reconstruct the signal provided some conditions are met. Some of the popular greedy reconstruction algorithms are the Orthogonal Matching Pursuit (OMP), the Subspace Pursuit (SP) and the Look Ahead Orthogonal Matching Pursuit (LAOMP). The LAOMP performs better than the OMP. However, when compared to the SP and the OMP, the computational complexity of LAOMP is higher. We introduce a modified version of the LAOMP termed as Reduced Look Ahead Orthogonal Matching Pursuit (Reduced LAOMP). Reduced LAOMP uses prior information from the results of the OMP and the SP in the quest to speedup the look ahead strategy in the LAOMP. Monte Carlo simulations of this algorithm deliver promising results.

Algorithm for Autonomous Reorganization of Mobile Wireless Camera Sensor Networks to Improve Coverage

In this paper, sensing coverage by wireless camera-embedded sensor networks (WCSNs), a class of directional sensors is studied. The proposed work facilitates the autonomous tuning of orientation parameters and displacement of camera-sensor nodes in the bounded field of interest (FoI), where the network coverage in terms of every point in the FoI is important. The proposed work is first of its kind to study the problem of maximizing coverage of randomly deployed mobile WCSNs which exploits their mobility. We propose an algorithm uncovered region exploration algorithm (UREA-CS) that can be executed in centralized and distributed modes. Further, the work is extended for two special scenarios: 1) to suit autonomous combing operations after initial random WCSN deployments and 2) to improve the network coverage with occlusions in the FoI. The extensive simulation results show that the performance of UREA-CS is consistent, robust, and versatile to achieve maximum coverage, both in centralized and distributed modes. The centralized and distributed modes are further analyzed with respect to the computational and communicational overheads.

Multi-agent Reinforcement Learning for Traffic Signal Control

Optimal control of traffic lights at junctions or traffic signal control (TSC) is essential for reducing the average delay experienced by the road users amidst the rapid increase in the usage of vehicles. In this paper, we formulate the TSC problem as a discounted cost Markov decision process (MDP) and apply multi-agent reinforcement learning (MARL) algorithms to obtain dynamic TSC policies. We model each traffic signal junction as an independent agent. An agent decides the signal duration of its phases in a round-robin (RR) manner using multi-agent Q-learning with either is an element of-greedy or UCB 3] based exploration strategies. It updates its Q-factors based on the cost feedback signal received from its neighbouring agents. This feedback signal can be easily constructed and is shown to be effective in minimizing the average delay of the vehicles in the network. We show through simulations over VISSIM that our algorithms perform significantly better than both the standard fixed signal timing (FST) algorithm and the saturation balancing (SAT) algorithm 15] over two real road networks.

An Alternating l(p) - l(2) Projections Algorithm (ALPA) for Speech Modeling using Sparsity Constraints

We address the problem of separating a speech signal into its excitation and vocal-tract filter components, which falls within the framework of blind deconvolution. Typically, the excitation in case of voiced speech is assumed to be sparse and the vocal-tract filter stable. We develop an alternating l(p) - l(2) projections algorithm (ALPA) to perform deconvolution taking into account these constraints. The algorithm is iterative, and alternates between two solution spaces. The initialization is based on the standard linear prediction decomposition of a speech signal into an autoregressive filter and prediction residue. In every iteration, a sparse excitation is estimated by optimizing an l(p)-norm-based cost and the vocal-tract filter is derived as a solution to a standard least-squares minimization problem. We validate the algorithm on voiced segments of natural speech signals and show applications to epoch estimation. We also present comparisons with state-of-the-art techniques and show that ALPA gives a sparser impulse-like excitation, where the impulses directly denote the epochs or instants of significant excitation.

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation: Application to Image Denoising

In big data image/video analytics, we encounter the problem of learning an over-complete dictionary for sparse representation from a large training dataset, which cannot be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm that exploits the inherent clustered structure of the training data and make use of a divide-and-conquer approach. The fundamental idea behind the algorithm is to partition the training dataset into smaller clusters, and learn local dictionaries for each cluster. Subsequently, the local dictionaries are merged to form a global dictionary. Merging is done by solving another dictionary learning problem on the atoms of the locally trained dictionaries. This algorithm is referred to as the split-and-merge algorithm. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy, which operates on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

A Fast and Fault-Tolerant Distributed Algorithm for Near-Optimal TDMA Scheduling in WSNs

The time division multiple access (TDMA) based channel access mechanisms perform better than the contention based channel access mechanisms, in terms of channel utilization, reliability and power consumption, specially for high data rate applications in wireless sensor networks (WSNs). Most of the existing distributed TDMA scheduling techniques can be classified as either static or dynamic. The primary purpose of static TDMA scheduling algorithms is to improve the channel utilization by generating a schedule of smaller length. But, they usually take longer time to schedule, and hence, are not suitable for WSNs, in which the network topology changes dynamically. On the other hand, dynamic TDMA scheduling algorithms generate a schedule quickly, but they are not efficient in terms of generated schedule length. In this paper, we propose a novel scheme for TDMA scheduling in WSNs, which can generate a compact schedule similar to static scheduling algorithms, while its runtime performance can be matched with those of dynamic scheduling algorithms. Furthermore, the proposed distributed TDMA scheduling algorithm has the capability to trade-off schedule length with the time required to generate the schedule. This would allow the developers of WSNs, to tune the performance, as per the requirement of prevalent WSN applications, and the requirement to perform re-scheduling. Finally, the proposed TDMA scheduling is fault-tolerant to packet loss due to erroneous wireless channel. The algorithm has been simulated using the Castalia simulator to compare its performance with those of others in terms of generated schedule length and the time required to generate the TDMA schedule. Simulation results show that the proposed algorithm generates a compact schedule in a very less time.