A Talk-Listen-Ack Beaconing Strategy for Neighbor Discovery Protocols in Wireless Sensor Networks

Neighbor discovery is a fundamental function for sensor networking. Sensor nodes discover each other by sending and receiving beacons. Although many time-slotted neighbor discovery protocols (NDPs) have been proposed, the theoretical discovery latency is measured by the number of time slots rather than the unit of time. Generally, the actual discovery latency of a NDP is proportional to its theoretical discovery latency and slot length, and inversely proportional to the discovery probability. Therefore, it is desired to increase discovery probability while reducing slot length. This task, however, is challenging because the slot length and the discovery probability are two conflicting factors, and they mainly depend on the beaconing strategy used. In this paper, we propose a new beaconing strategy, called talk-listen-ack beaconing (TLA). We analyze the discovery probability of TLA by using a fine-grained slot model. Further, we also analyze the discovery probability of TLA that uses random backoff mechanism to avoid persistent collisions. Simulation and experimental results show that, compared with the 2-Beacon approach that has been widely used in time-slotted NDPs, TLA can achieve a high discovery probability even in a short time slot. TLA is a generic beaconing strategy that can be applied to different slotted NDPs to reduce their discovery latency.

A Combinatorial Approach to the Computation of the Fractional Edge Dimension of Graphs

E. Yi recently introduced the fractional edge dimension of graphs. It has many applications in different areas of computer science such as in sensor networking, intelligent systems, optimization, and robot navigation. In this paper, the fractional edge dimension of vertex and edge transitive graphs is calculated. The class of hypercube graph Qn with an odd number of vertices n is discussed. We propose the combinatorial criterion for the calculation of the fractional edge dimension of a graph, and hence applied it to calculate the fractional edge dimension of the friendship graph Fk and the class of circulant graph Cn(1,2).

On 2-metric resolvability in rotationally-symmetric graphs

The 2-metric resolvability is an extension of metric resolvability in graphs having several applications in intelligent systems for example network optimization, robot navigation and sensor networking. Rotationally symmetric graphs are important in intelligent networks due to uniform rate of data transformation to all nodes. In this article, 2-metric dimension of rotationally symmetric plane graphs Rn, Sn and Tn is computed and found to be independent of the number of vertices.

On fault-tolerant partition dimension of graphs

Fault-tolerant resolving partition is natural extension of resolving partitions which have many applications in different areas of computer sciences for example sensor networking, intelligent systems, optimization and robot navigation. For a nontrivial connected graph G (V (G) , E (G)), the partition representation of vertex v with respect to an ordered partition Π = {Si : 1 ≤ i ≤ k} of V (G) is the k-vector r ( v | Π ) = ( d ( v , S i ) ) i = 1 k , where, d (v, Si) = min {d (v, x) |x ∈ Si}, for i ∈ {1, 2, …, k}. A partition Π is said to be fault-tolerant partition resolving set of G if r (u|Π) and r (v|Π) differ by at least two places for all u ≠ v ∈ V (G). A fault-tolerant partition resolving set of minimum cardinality is called the fault-tolerant partition basis of G and its cardinality the fault-tolerant partition dimension of G denoted by P ( G ) . In this article, we will compute fault-tolerant partition dimension of families of tadpole and necklace graphs.