Arunabha Sen

Relay node placement in large scale wireless sensor networks

Scalability and extended lifetime are two critical design goals of any large scale wireless sensor network. A two-tiered network model has been proposed recently for this purpose. This is a cluster-based network model composed of relay and sensor nodes. Relay nodes are placed in the playing field to serve as cluster heads and to form a connected network topology for information dissemination at the higher tier. The relay nodes are capable of aggregating data packets from the sensor nodes in their clusters and transmitting them to the sink node via wireless multi-hop paths. In this paper, we study the relay node placement problem in large scale wireless sensor networks. Our objective is to place the fewest number of relay nodes in the playing field of a sensor network such that (1) each sensor node can communicate with at least one relay node and (2) the network of relay nodes is connected. However, placement strategies realizing goals (1) and (2) do not provide any fault-tolerance as the network may lose functionality after failure of some of the relay nodes. In order to incorporate fault-tolerance in such a network, we ensure that every sensor node is able to communicate with at least two relay nodes and the induced network topology is 2-connected. This strategy will ensure survivability of the network in the event of single fault, in lieu of higher relay node placement cost. We formulate the relay node placement in wireless sensor networks as two optimization problems: (i) Connected Relay Node Single Cover (CRNSC) problem and (ii) 2-Connected Relay Node Double Cover (2CRNDC) problem. We present two polynomial time approximation algorithms to solve the CRNSC problem. We prove that the ratio of the number of relay nodes needed by the approximation algorithm to the number of relay nodes needed by the optimal algorithm is bounded by 8 for the first algorithm and 4.5 for the second. In addition, for the 2CRNDC problem we provide two approximation algorithms with performance bounds 6 and 4.5, respectively.

A new model for scheduling packet radio networks

Packet radio networks are modeled as arbitrary graphs by most researchers. In this paper we show that an arbitrary graph is an inaccurate model of the radio networks. This is true because there exists a large class of graphs which will not model the radio networks. Radio networks can be modeled accurately by a restricted class of graphs called the planar point graphs. Since the radio networks can accurately be modeled only by a restricted class of graphs, the NP-completeness results for scheduling using an arbitrary graph as the model, do not correctly reflect the complexity of the problem. In this paper we study the broadcast scheduling problem using the restricted class as the model. We show that the problem remains NP-complete even in this restricted domain. We give an O(n log n) algorithm when all the transceivers are located on a line.

Finding a path subject to many additive QoS constraints

A fundamental problem in quality-of-service (QoS) routing is to find a path between a source-destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and m edges with K additive QoS parameters associated with each edge, for any constant K ≥ 2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K = 2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple O(Km + nlogn) time K -approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m(n/e)K-1).3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(n log n + m(H/e)K-1) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used.

Region-based connectivity - a new paradigm for design of fault-tolerant networks

The studies in fault-tolerance in networks mostly focus on the connectivity of the graph as the metric of faulttolerance. If the underlying graph is k-connected, it can tolerate up to k — 1 failures. In measuring the fault tolerance in terms of connectivity, no assumption regarding the locations of the faulty nodes are made - the failed nodes may be close to each other or far from each other. In other words, the connectivity metric has no way of capturing the notion of locality of faults. However in many networks, faults may be highly localized. This is particularly true in military networks, where an enemy bomb may inflict massive but localized damage to the network. To capture the notion of locality of faults in a network, a new metric region-based connectivity (RBC) was introduced in [1]. It was shown that RBC can achieve the same level of fault-tolerance as the metric connectivity, with much lower networking resources. The study in [1] was restricted to single region fault model (SRFM), where faults are confined to one region only. In this paper, we extend the notion of RBC to multiple region fault model (MRFM), where faults are no longer confined to a single region. As faults in MRFM are still confined to regions, albeit multiple of them, it is different from unconstrained fault model where no constraint on locality of faults is imposed. The MRFM leads to several new concepts, such as region-disjoint paths and region cuts. We show that the classical result, the maximum number of node-disjoint paths between a pair of nodes is equal to the minimum number of nodes whose removal disconnects the pair, is no longer valid when region-disjoint paths and region cuts are considered. We prove that the problems of finding (i) the maximum number of region-disjoint paths between a pair of nodes, and (ii) minimum number of regions whose removal disconnect a pair of nodes, are both NP-complete. We provide heuristic solution to these two problems and evaluate their efficacy by comparing the results with optimal solutions.

Supercube: An optimally fault tolerant network architecture

SummaryA new class of interconnection network topology is proposed for parallel and distributed processing. The attractive features of this class include (a) the network can be constructed for any number of computing nodes, (b) the network is incrementally expandable, i.e., a new node can easily be added to the existing network, (c) it has good fault-tolerant characteristics (measured by the connectivity of the network graph) and (d) it has small delay characteristics (measured by the diameter of the network graph). The node connectivity of the network is equal to the minimum node degree. In this sense the network is optimally fault-tolerant.

The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs

In this paper we study the Optimal Cost Chromatic Partition (OCCP) problem for trees and interval graphs. The OCCP problem is the problem of coloring the nodes of a graph in such a way that adjacent nodes obtain different colors and that the total coloring costs are minimum.

Broadcast scheduling algorithms for radio networks

We investigate scheduling problems associated with radio networks using models based on graphs. Scheduling in networks is typically solved using graph coloring algorithms. In many cases the coloring algorithms are based on simplifying assumptions about the network structure. We show the limitations of the current models and propose modifications. The current models do not address the nonuniform transceiver/transmitter networks and they over-restrict transceiver interconnections. We develop algorithms which are more specific to the domain of radio network scheduling. We compare the performance of the earlier algorithms to our algorithms. The results are analyzed with respect to both execution time and quality of solution for networks of various sizes and densities.

On a graph partition problem with application to VLSI layout

We discuss a graph partition problem with application to VLSI layout. It is not difficult to show that the general partition problem is NPComplete, so we restrict our attention to some special classes of graphs. A graph is called a circZe graph if the nodes of the graph represent the chords of a circle and there is an edge between the two nodes if the corresponding chords intersect. Supowit in [17] had posed the partition problem of circle graphs as an open problem. However, it is also not too difficult to show that the partition problem on circle graphs remains NP-Complete. We give an integer linear programming formulation for the general graph par-

On disjoint path pairs with wavelength continuity constraint in WDM networks

In a WDM optical network, each fiber link can carry a certain set of wavelengths /spl Lambda/= {/spl lambda//sub 1/,/spl lambda//sub 2/,...,/spl lambda//sub W/}. One scheme for tolerating a single link failure (or node failure) in the network is the path protection scheme, which establishes an active path and a link-disjoint (or node-disjoint) backup path, so that in the event of a link failure (node failure) on the active path, data can be quickly re-routed through the backup path. We consider a dynamic scenario, where requests to establish active-backup paths between a specified source-destination node pair arrive sequentially. If a link-disjoint (node-disjoint) active-backup path pair is found at the time of the request, the paths are established; otherwise, the request is blocked. In this scenario, at the time a request arrives, not every fiber link will have all W wavelengths available for new call establishment, as some of the wavelengths may already have been allocated to earlier requests and communication through these paths may still be in progress. We assume that the network nodes do not have any wavelength converters. This paper studies the existence of a pair of link-disjoint (node-disjoint) active-backup paths satisfying the wavelength continuity constraint between a specified source-destination node pair. First we prove that both the link-disjoint and node-disjoint versions of the problem are NP-complete. Then we focus on the link-disjoint version and present an approximation algorithm and an exact algorithm for the problem. Finally, through our experimental evaluations, we demonstrate that our approximation algorithm produces near-optimal solutions in almost all of the instances of the problem in a fraction of the time required by the exact algorithm.

Fault-Tolerance in Sensor Networks: A New Evaluation Metric

A new metric for measuring the fault-tolerance capability of a multihop wireless sensor network is introduced in this paper. Most of the studies on fault-tolerance in sensor networks use connectivity as the metric of fault-tolerance. If the underlying network is k-connected, it can tolerate up to k − 1 failures. In measuring fault tolerance in terms of connectivity, no assumption regarding the locations of the failed sensor nodes is made they may be very close to each other or very far from each other. In other words, the connectivity metric fails to capture any notion of locality of faults. However, in sensor networks, it is highly likely that the faults will be localized. This is particularly true in military applications, where an enemy bomb may inflict massive but localized damage to the sensor network. To capture the notion of locality in fault-tolerance, we introduce the notion of region-based connectivity. The region-based connectivity of a network may be informally defined to be the minimum number of nodes within a region whose failure will disconnect the network. Obviously, the notion of region-based connectivity is tied to the notion of a region. A region may be defined in several different ways and they are discussed in detail in the paper. The attractive feature of the region-based connectivity as the fault-tolerance metric is that it can achieve the same level of fault-tolerance as the traditional metric connectivity, but requires much lower transmission power for the sensor nodes. We provide both analytical as well as extensive simulation results to support our claim.