Ehab S. Elmallah

On The Reliability of Wireless Sensor Networks

In wireless sensor networks (WSN), reliable monitoring of a phenomenon (or event detection) depends on the collective data provided by the target cluster of sensors and not on any individual node. In this paper we define a WSN reliability measure that considers the aggregate flow of sensor data into a sink node (gateway or cluster head). Given an estimation of the data generation rate and the failure probability of each sensor, we formulate the reliability measure and show that computing this measure for an arbitrary WSN is WSN. We then consider some special cases where we can either compute or approximate (bound) the reliability using an efficient algorithm. Finally, we present some numerical results that demonstrate some of the applications of our algorithms. Reliability evaluation tools are important in the context of design and analysis of sensitive information gathering sensor networks.

A flow-based reliability measure for wireless sensor networks

In Wireless Sensor Networks (WSNs), reliable monitoring of a phenomenon depends on the collective data provided by clusters of sensor nodes and not on any individual node. Thus, the design of a WSN may impose constraints on the minimum average data rate that is required to be gathered from the sensor nodes and delivered to a sink node. In this paper, we define a WSN reliability measure that quantifies the likelihood that a network can deliver such minimum required data flow where the individual sensor components are subject to random failures. Given a specification of the average data rate generated by each sensor node, the operation probability of each sensor and the connectivity graph of a WSN, we formulate the reliability measure and show that the problem of computing the exact reliability of any arbitrary WSN is #P-hard. Thus, it is unlikely that an efficient algorithm for computing exact solutions exists. We present two exponential algorithms for handling networks with arbitrary topologies. We then consider some special cases where we can either compute or approximate the reliability efficiently. Finally, we present numerical results that demonstrate potential applications of the devised algorithms in WSN design.

On two dual classes of planar graphs

Abstract A planar graph G is delta-wye “Δ- Y ” reducible if G can be reduced to an edge by a sequence of Δ- Y , series, parallel and degree-1 reductions. Politof characterizes Δ- Y reducible graphs in terms of forbidden homeomorphic subgraphs. A wye-delta “ Y -Δ” reducible graph is one that can be reduced to an edge by a sequence of Y -Δ, series, parallel and degree-1 reductions. Y -Δ reducible graphs are all partial 3-trees. Recently, Arnborg and Proskurowski have shown confluent reductions which are both necessary and sufficient for the recognition of partial 3-trees. In this paper we note that Δ- Y graphs are the planar duals of Y -Δ graphs. We exploit this duality and the known reduction rules for partial 3-trees to characterize both classes of graphs using forbidden minors. The result yields a shorter proof of Politofs result. In addition, we give linear time algorithms for recognizing such graphs and for embedding any Δ- Y graph in a 4-tree. These algorithms complement many known linear time algorithms for solving some hard network problems on graphs given their embedding in a k-tree for some fixed k .

Supporting QoS routing in mobile ad hoc networks using probabilistic locality and load balancing

Harnessing the time varying topological aspect of mobile ad hoc networks so as to support Quality of Service (QoS) measures is a challenging problem. In this paper we develop and investigate the use of a simple spatial probabilistic locality model to enhance the performance of current on-demand routing algorithms. To explore the applicability of our approach, we examine two basic routing problems. The first problem calls for evaluating the likelihood that a given source-destination route exists, given that each mobile host on the route can be in any position of its locality set. The second problem calls for choosing the most probable route between a given source-destination pair that avoids traffic bottlenecks. In each case, we formalize a suitable problem, and devise an efficient solution strategy.

Logarithmic keying of communication networks

Consider a communication network where each process needs to securely exchange messages with its neighboring processes. In this network, each sent message is encrypted using one or more symmetric keys that are shared only between two processes: the process that sends the message and the neighboring process that receives the message. A straightforward scheme for assigning symmetric keys to the different processes in such a network is to assign each process O(d) keys, where d is the maximum number of neighbors of any process in the network. In this paper, we present a more efficient scheme for assigning symmetric keys to the different processes in a communication network. This scheme, which is referred to as logarithmic keying, assigns O(log d) symmetric keys to each process in the network. We show that logarithmic keying can be used in rich classes of communication networks that include star networks, acyclic networks, limited- cycle networks, and planar networks.

A power-aware admission control scheme for supporting the assured forwarding model in CDMA cellular networks

The differentiated services (DiffServ) architecture for provisioning quality of service (QoS) in the Internet provides a flexible framework for supporting a variety of services in heterogeneous environments. The assured forwarding (AF) per hop behaviour is a means of providing differential treatment of various DiffServ classes through achieving higher forwarding probabilities for higher priority classes. Extending the AF model to support fine grain QoS specification in W-CDMA environments allows mobile users in third-generation systems to benefit from the economical savings made possible by resource sharing among different classes of aggregated traffic. We consider extending the AF model to support the delivery of quasi constant bit-rate (QCBR) traffic streams on the downlink. In our study, each QCBR stream is assumed to have a prescribed average bit-rate and time duration, and is expected to be transmitted to completion without interruption at the requested bit-rate. The availability of such a service is beneficial for transmitting real-time traffic to mobile devices with limited power and buffering resources. The proposed mechanisms are based on integrating a suitable power-sharing structure for achieving differential treatment between classes with a crude power prediction algorithm for estimating the probability that no forced termination will occur at certain instants in the future. We compare the performance of a non-predictive scheme with a predictive scheme for different AF classes and source information bit-rates. Our results show that significant improvement in the forwarding probability, throughput, and power utilization for the DiffServ classes can be attained using the predictive scheme.

Polygon Graph Recognition

For any fixed integerk?2, define the class ofk-polygon graphs as the intersection graphs of chords inside a convexk-polygon, where the endpoints of each chord lie on two different sides. The case wherek=2 is degenerate; for our purpose, we view any pair of parallel lines as a 2-polygon. Hence, polygon graphs are all circle graphs. Interest in such graphs arises since a number of intractable problems on circle graphs can be solved in polynomial time onk-polygon graphs, for any fixedk, given a polygon representation of the input graph. In this paper we show that determining whether a given circle graph is ak-polygon graph, for any fixedk, can be solved inO(4kn2) time. The algorithm exploits the structure of a decomposition tree of the input graph and produces ak-polygon representation, if one exists. In contrast, we show that determining the minimum value ofkis NP-complete.

Independence and domination in polygon graphs

Abstract Given an integer k, k≥3, we define the class of k-polygon graphs to be the intersection graphs of straight-line chords inside a convex k-gon. Thus, permutation graphs form a proper subset of any such class. Moreover, circle graphs = ∪∞k=3 k-polygon graphs. In this paper, we show polynomial time exact algorithms for solving the maximum r-independent set problem (finding a maximum subset of vertices that can be partitioned into r independent sets) and the minimum dominating set problem on k-polygen graphs, for any fixed k.

Non-Bifurcated Routing in Wireless Multi-Hop Mesh Networks

In this paper we consider traffic routing in 802.11- based multi-hop wireless mesh networks (WMNs). Interest in such networks arises since they offer flexible, and cost effective means of providing Internet connectivity to communities of subscribers. Successful deployment of such networks, however, hinges on the ability of the network to serve subscribers at the data rates specified by service agreements, as well as providing quality of service to certain key traffic types, such as TCP traffic, delay-jitter sensitive traffic, and traffic that requires synchronized delivery to end users. Since delays on different routes in such networks may vary widely, routing of the above traffic types can potentially benefit from non-bifurcated routing schemes that do not split flows among multiple paths. In this paper, we formalize the problem of non-bifurcated routing, while meeting subscriber demands, as an optimization problem. We present a heuristic algorithm that utilizes results from the theory of maximum flows, and insights into the routing problem to obtain efficient solutions. Simulation experiments indicate improved achieved throughput, and delay-jitter results over the use of the standard Dynamic Source Routing (DSR) algorithm.

Optimal Dispersal of Certificate Chains

We consider a network where users can issue certificates that identify the public keys of other users in the network. The issued certificates in a network constitute a set of certificate chains between users. A user u can obtain the public key of other user v from a certificate chain from u to v in the network. For the certificate chain from u to v, u is called the source of the chain and v is called the destination of the chain. Certificates in each chain are dispersed between the source and destination of the chain such that the following condition holds. If any user u needs to securely send messages to any other user v in the network, then u can use the certificates stored in u and v to obtain the public key of v (then u can use the public key of v to set up a shared key with v to securely send messages to v). The cost of dispersing certificates in a set of chains among the source and destination users in a network is measured by the total number of certificates that need to be stored in all users. A dispersal of a set of certificate chains in network is optimal if no other dispersal of the same chain set has a strictly lower cost. In this paper, we show that the problem of computing optimal dispersal of a given chain set is NP-Complete. We also present three polynomial-time algorithms that compute optimal dispersals for three special classes of chain sets.