B. S. Panda

A linear time recognition algorithm for proper interval graphs

We propose a linear time recognition algorithm for proper interval graphs. The algorithm is based on certain ordering of vertices, called bicompatible elimination ordering (BCO). Given a BCO of a biconnected proper interval graph G, we also propose a linear time algorithm to construct a Hamiltonian cycle of G.

Intersection graphs of vertex disjoint paths in a tree

Abstract Two characterizations of intersection graphs of vertex disjoint paths in a tree, one in terms of maximal clique separator and the other in terms of minimal forbidden subgraphs, are presented. A polynomial recognition algorithm for this class is suggested.

An incremental power greedy heuristic for strong minimum energy topology in wireless sensor networks

Given a set of sensors in the plane, the strong minimum energy topology (SMET) problem is to assign transmit power to each sensor such that the resulting topology containing only bidirectional links is strongly connected. This problemis known to be NP-hard. As this problem is verymuch significant from application point of view, several heuristic algorithms have been proposed. In this paper, we propose a new incremental power greedy heuristic for SMET problem, called Kruskal-incremental power greedy heuristic. We compare Kruskal-incremental power greedy heuristic with Prim-incremental power greedy heuristic, one of the most popular heuristics available in the literature, through extensive simulation. The simulation results suggest that Kruskal-incremental power greedy heuristic outperforms on an average the Prim-incremental power greedy heuristic.

Performance Evaluation of a Two Level Error Recovery Scheme for Distributed Systems

Rollback recovery schemes are used in fault-tolerant distributed systems to minimize the computation loss incurred in the presence of failures. One-level recovery schemes do not consider the different types of failures and their relative frequency of occurrence, thereby tolerating all failures with the same overhead. Two-level recovery schemes aim to provide low overhead protection against more probable failures, providing protection against other failures with possibly higher overhead. In this paper, we have analyzed a two-level recovery scheme due to Vaidya taking probability of task completion on a system with limited repairs as the performance metric.

New linear time algorithms for generating perfect elimination orderings of chordal graphs

We propose two linear time algorithms: maximum cardinality depth-first search (MCDFS) and maximum cardinality breadth-first search (MCBFS), which are variants of depth-first search and breadth-first search, respectively, to generate perfect elimination orderings of chordal graphs.

Energy-Efficient Greedy Forwarding Protocol for Wireless Sensor Networks

In a wireless sensor network, as the sensor nodes have limited energy, it is important to minimize nodal energy consumption due to message communication to extend the network lifetime. Existing forwarding protocols either do not consider network performance and energy saving jointly, or they are not distributed. In this paper, we propose a hybrid approach, called minimum consumption maximum remaining energy (MIN-MAX-E) forwarding, which combines minimum energy consumption of transmitter-receiver pair along with maximum remaining energy of the receiver in making a relay node selection decision. Extensive simulation studies show that the proposed algorithm offers a significantly improved energy saving performance with respect to the existing energy-aware approaches.

L(2,1)-labeling of perfect elimination bipartite graphs

Abstract An L ( 2 , 1 ) -labeling of a graph G is an assignment of nonnegative integers, called colors, to the vertices of G such that the difference between the colors assigned to any two adjacent vertices is at least two and the difference between the colors assigned to any two vertices which are at distance two apart is at least one. The span of an L ( 2 , 1 ) -labeling f is the maximum color number that has been assigned to a vertex of G by f . The L ( 2 , 1 ) -labeling number of a graph G , denoted as λ ( G ) , is the least integer k such that G has an L ( 2 , 1 ) -labeling of span k . In this paper, we propose a linear time algorithm to L ( 2 , 1 ) -label a chain graph optimally. We present constant approximation L ( 2 , 1 ) -labeling algorithms for various subclasses of chordal bipartite graphs. We show that λ ( G ) = O ( Δ ( G ) ) for a chordal bipartite graph G , where Δ ( G ) is the maximum degree of G . However, we show that there are perfect elimination bipartite graphs having λ = Ω ( Δ 2 ) . Finally, we prove that computing λ ( G ) of a perfect elimination bipartite graph is NP-hard.

Boruvka-Incremental Power Greedy Heuristic for Strong Minimum Energy Topology in Wireless Sensor Networks

Given a set of sensors, the strong minimum energy topology (SMET) problem is to assign transmission range to each sensor node so that the sum of the transmission range for all the sensor is minimum subject to the constraint that the network is strongly connected (there is a directed path between every pair of nodes in the Network). This problem is known to be NP-hard. As this problem has lots of practical applications, several approximation algorithms and heuristics have been proposed. In this paper, we propose a new heuristic called Boruvka-incremental power greedy heuristic based on the Boruvka algorithm for the minimum spanning tree (MST) problem for solving the SMET problem. We compare the performance of the Boruvka-incremental power greedy heuristic with Kruskal-incremental power greedy heuristic and Prim-incremental power greedy heuristic. Extensive simulation results illustrate that Boruvka heuristic outperforms the Kruskal-incremental power greedy heuristic and Prim-incremental power greedy heuristic. We have also proved that apart from providing significant improvement in terms of average power savings, Boruvka incremental power greedy heuristic takes O(n) time for planar graphs as compared to O(n log n) time taken by Kruskal-incremental power greedy heuristic and O(n2) time taken by Prim-incremental power greedy heuristic, where n is the number of nodes in the network.

Algorithmic Aspects of Disjunctive Domination in Graphs

For a graph \(G=(V,E)\), a set \(D\subseteq V\) is called a disjunctive dominating set of G if for every vertex \(v\in V\setminus D\), v is either adjacent to a vertex of D or has at least two vertices in D at distance 2 from it. The cardinality of a minimum disjunctive dominating set of G is called the disjunctive domination number of graph G, and is denoted by \(\gamma _{2}^{d}(G)\). The Minimum Disjunctive Domination Problem (MDDP) is to find a disjunctive dominating set of cardinality \(\gamma _{2}^{d}(G)\). Given a positive integer k and a graph G, the Disjunctive Domination Decision Problem (DDDP) is to decide whether G has a disjunctive dominating set of cardinality at most k. In this article, we first propose a polynomial time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a \((\ln (\Delta ^{2}+\Delta +2)+1)\)-approximation algorithm for MDDP, where \(\Delta \) is the maximum degree of input graph \(G=(V,E)\) and prove that MDDP can not be approximated within \((1-\epsilon ) \ln (|V|)\) for any \(\epsilon >0\) unless NP \(\subseteq \) DTIME\((|V|^{O(\log \log |V|)})\). Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree 3.

A linear time algorithm to compute a minimum restrained dominating set in proper interval graphs

A set D ⊆ V is a restrained dominating set of a graph G = (V, E) if every vertex in V\D is adjacent to a vertex in D and a vertex in V\D. Given a graph G and a positive integer k, the restrained domination problem is to check whether G has a restrained dominating set of size at most k. The restrained domination problem is known to be NP-complete even for chordal graphs. In this paper, we propose a linear time algorithm to compute a minimum restrained dominating set of a proper interval graph. We present a polynomial time reduction that proves the NP-completeness of the restrained domination problem for undirected path graphs, chordal bipartite graphs, circle graphs, and planar graphs.