Abhishek Kashyap

Relay Placement for Higher Order Connectivity in Wireless Sensor Networks

Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is 2-connected. The problem is NP -hard. In this paper we develop O(1)-approximation algorithms that find close to optimal solutions in time O((kn)) for achieving k-edge connectivity of n nodes. The worst case approximation guarantee is 10, but the algorithm produces solutions that are far better than this bound suggests. We also consider extensions to higher dimensions, and the scheme that we develop for points in the plane, yields a bound of 2dMST where dMST is the maximum degree of a minimum-degree Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles). We also prove that if the sensors are uniformly and identically distributed in a unit square, the expected number of relay nodes required goes to zero as the number of sensors goes to infinity.

Integrated topology control and routing in wireless optical mesh networks

We study the problem of integrated topology control and routing in Free Space Optical (FSO) mesh backbone networks. FSO links are high-bandwidth, low interference links that can be set-up very fast, making them suitable for mesh networking. FSO networks are highly constrained by interface constraints, i.e., constraints on the number of FSO links a node can establish. We prove the problem to be NP-Hard and propose efficient algorithms for integrated topology control and single-path or multi-path routing.

Relay placement for fault tolerance in wireless networks in higher dimensions

In this paper we consider the problem of adding the smallest number of additional (relay) nodes to a network of static nodes with limited communication range so that the induced communication graph is 2-connected (we consider both edge and vertex connectivity). The problem is NP-hard. We develop algorithms that find close to optimal solutions for both edge and vertex connectivity. We prove the algorithms have an approximation ratio of 2M for nodes distributed in a d-dimensional Euclidean space, where M is the maximum node degree of a Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles).

Routing and traffic engineering in hybrid RF/FSO networks

We provide a routing framework for hybrid RF/FSO backbone networks, utilizing the characteristics of RF and free space optical (FSO) links. FSO links offer higher bandwidth and security, while RF links offer more reliability. We propose the concept of criticality index for different classes of traffic and providing obscuration-tolerant paths to the traffic in a weighted max-min fair way. We provide an optimal algorithm for the case where a traffic demand can be routed along multiple paths. The problem of routing unsplittable traffic is NP-hard, so we propose efficient heuristics for routing them. We do extensive simulations to demonstrate that our algorithms outperform the algorithms currently in use.

WSN18-4: Integrated Backup Topology Control and Routing of Obscured Traffic in Hybrid RF/FSO Networks

We propose a framework for providing instantaneous backup to traffic in a hybrid RF/FSO mesh network. Free space optical (FSO) links have high bandwidth and security, making them suitable for use in backbone networks. RF links have low bandwidth, but offer high reliability in conditions where FSO links are obscured. Thus, RF links are primarily used to provide instantaneous backup to traffic flowing on FSO links. We propose a framework to model FSO link failures due to obscuration, and propose algorithms for integrated topology control of RF links and routing for maximizing the backup provided. We do extensive simulations to demonstrate that the performance of RF topology and routing computed using our algorithms is much better than the case of having the same RF and FSO topologies and routes.

Two-phase routing, scheduling and power control for wireless mesh networks with variable traffic

We consider the problem of joint routing, scheduling and transmission power assignment in multi-hop wireless mesh networks with unknown traffic. We assume the traffic is unknown, but the traffic matrix, which specifies the traffic load between every source-destination pair in the network, always lies inside a polytope defined by hose model constraints. The objective is to minimize the maximum of the total transmission power in the network over all traffic matrices in a given polytope. We propose efficient algorithms that compute a two-phase routing, schedule and power assignment, and prove the solution to be 3-approximation with respect to an optimal two-phase routing, scheduling and power assignment. We show via extensive simulations that the proposed algorithm has good performance at its worst operating traffic compared to an algorithm optimized for that traffic.

Robust Routing with Unknown Traffic Matrices

In this paper, we present an algorithm for intra-domain traffic engineering. We assume that the traffic matrix, which specifies traffic load between every source-destination pair in the network, is unknown and varies with time, but that always lies inside an explicitly defined region. Our goal is to compute a fixed robust routing with best worst case performance for all traffic matrices inside the bounding region. We formulate this problem as a semi-infinite programming problem. Then, we focus on a special case with practical merits, where (1) the traffic matrix region is assumed to be a polytope specified by a finite set of linear inequalities, and (2) our objective is to find the routing that minimizes the maximum link utilization. Under these assumptions, the problem can be formulated as a polynomial size linear programming (LP) problem with finite number of constraints. We further consider two specific set of constraints for the traffic matrix region. The first set is based on the hose model and limits the total traffic rate of network point of presence (PoP) nodes. The second set is based on the pipe model and limits the traffic between source-destination pairs. We study the effectiveness of each set of constraints using extensive simulations.

Relay Placement and Movement Control for Realization of Fault-Tolerant Ad Hoc Networks

Wireless communication is a critical component of battlefield networks. Nodes in a battlefield network exist in hostile environments and thus fault-tolerance against node and link failures is a desirable property for the communication topology of such networks. The network nodes are mobile and move depending on the objective they try to achieve; thus the topology needs to be re-established periodically. The transmitters used for communication have a fixed transmission range, so additional nodes are required for the construction of a fault-tolerant topology among network nodes. As the network nodes move, the additional nodes need to be moved as well; and it is desirable to move them a minimum amount to re-establish the topology as quickly as possible. We propose algorithms for minimizing the number of additional nodes required and the distance they need to move for construction of a topology with desired levels of fault-tolerance. We show via extensive simulations that the algorithms perform much better than an algorithm that does not take minimizing the movement of additional nodes into account.

Relay placement for minimizing congestion in wireless backbone networks

Wireless optical networks are being increasingly used in the backbone of hierarchical ad hoc networks. We consider the problem of minimizing the congestion in wireless optical (FSO) backbone networks by placing controllable relay nodes. We propose algorithms for placement of relays in the network under node interface constraints. The interfaces at each backbone node are limited, thus limiting the number of neighbors a node can have. We come up with algorithms to formulate the problem as a constrained knapsack problem, and propose algorithms to solve it. We use the mathematical technique of rollout to achieve better performance than the heuristics. We show by simulations that our algorithms significantly outperform some greedy algorithms, and a small number of relay nodes (when placed using our algorithms) can lead to a significant reduction in the congestion in the network

CAM04-6: Single-Path Routing of Time-varying Traffic

We consider the problem of finding a single-path intra-domain routing for time-varying traffic. We characterize the traffic variations by a finite set of traffic profiles with given non-zero fractions of occurrence. Our goal is to optimize the average performance over all of these traffic profiles. We solve the optimal multi-path version of this problem using linear programming and develop heuristic single-path solutions using randomized rounding and iterated rounding. We analyze our single-path heuristic (finding the optimal single-path routing is NP-hard), and prove that the randomized rounding algorithm has a worst case performance bound of O(log(KN)/log(log(KN))) compared to the optimal multi-path routing with a high probability, where K is the number of traffic profiles, and N the number of nodes in the network. Further, our simulations show the iterated rounding heuristics perform close to the optimal multi-path routing on a wide range of measured ISP topologies, in both the average and the worst-case. Overall, these results are extremely positive since they show that in a wide-range of practical situations, it is not necessary to deploy multi-path routing; instead, an appropriately computed single-path routing is sufficient to provide good performance.