Barun Gorain

Line sweep coverage in wireless sensor networks

Traditional coverage in wireless sensor networks requires continuous monitoring of target objects or regions. Unlike traditional coverage, periodic monitoring by a set of mobile sensor nodes is sufficient in sweep coverage. The sweep coverage problem for covering a set of points is NP-hard and it cannot be approximated within a factor of 2 [15]. The sweep coverage problem for a given bounded region is also NP-hard [11]. In this paper, we study sweep coverage for covering a set of line segments on a plane. We prove that the problem is NP-hard and cannot be approximated within a factor 2. Our proposed algorithm achieves the best possible approximation factor 2. As an application of line sweep coverage problem we formulate a data gathering problem, where minimum number of data mules periodically collect data from a set of mobile sensor nodes. The mobile sensor nodes arbitrarily move along their paths, which are line segments. We prove that this problem is NP-hard and propose a 3 approximation algorithm to solve it.

Approximation algorithm for sweep coverage on graph

The objective of sweep coverage problem is to find the minimum number of mobile sensors to ensure periodic monitoring for a given set of points of interest. In this paper we remark on the flaw of the approximation algorithms proposed in paper 16] for sweep coverage with mobile sensors and propose a 3-approximation algorithm to guarantee sweep coverage of vertices of a graph. We propose a solution of the problem when vertices of a graph have different sweep periods and processing times. The approximation factor of the proposed solution is O ( log ? ? ) , where ? is the ratio of the maximum and minimum sweep periods among the vertices. We prove that if velocities of the mobile sensors are different, it is impossible to give any constant factor approximation algorithm to solve the sweep coverage problem unless P = NP . Remarked on the flaw of approximation algorithms in the previous study and proposed a 3-approximation algorithm.Generalized the proposed algorithm when vertices of the graph have different sweep periods and processing times.Inapproximability result is proved for the sweep coverage problem with mobile sensors having different velocities.

Solving energy issues for sweep coverage in wireless sensor networks

Sweep coverage provides solutions for the applications in wireless sensor networks, where periodic monitoring is sufficient instead of continuous monitoring. The objective of the sweep coverage problem is to minimize the number of sensors required in order to guarantee sweep coverage for a given set of points of interest on a plane. Instead of using only mobile sensors for sweep coverage, use of both static and mobile sensors can be more effective in terms of energy utilization. In this paper, we introduce two variations in sweep coverage problem, where energy consumption by the sensors is taken into consideration. First, an energy efficient sweep coverage problem is proposed, where the objective is to minimize energy consumption by a set of sensors (mobile and/or static) with guaranteed sweep coverage. We prove that the problem is NP-hard and cannot be approximated within a factor of 2. An 8-approximation algorithm is proposed to solve the problem. A 2-approximation algorithm is also proposed for a special case. Second, an energy restricted sweep coverage problem is proposed, where the objective is to find the minimum number of mobile sensors to guarantee sweep coverage subject to the condition that the energy consumption by a mobile sensor in a given time period is bounded. We propose a (5+2)-approximation algorithm to solve this NP-hard problem.

Energy Efficient Sweep Coverage with Mobile and Static Sensors

Sweep coverage provides solution for the applications in wireless sensor networks, where periodic monitoring is sufficient instead of continuous monitoring. For a given set of points in the plane, the objective of the sweep coverage problem is to minimize number of sensors required in order to guarantee sweep coverage for a given set of points of interest. Instead of using only mobile sensors for sweep coverage, use of both static and mobile sensors can be more effective in terms of energy utilization. In this paper we introduce the EEGSweep coverage problem, where objective is to minimize energy consumption by a set of sensors (mobile and/or static) with guaranteed sweep coverage for a given set of points. We prove that the EEGSweep coverage problem is NP-hard and cannot be approximated within a factor of 2. We propose an 8-approximation algorithm to solve the problem. A 2-approximation algorithm is also proposed for a special case of this problem.

Finding the Size of a Radio Network with Short Labels

The number of nodes of a network, called its size, is one of the most important network parameters. Knowing the size (or a good upper bound on it) is a prerequisite of many distributed network algorithms, ranging from broadcasting and gossiping, through leader election, to rendezvous and exploration. A radio network is a collection of stations, called nodes, with wireless transmission and receiving capabilities. It is modeled as a simple connected undirected graph whose nodes communicate in synchronous rounds. In each round, a node can either transmit a message to all its neighbors, or stay silent and listen. At the receiving end, a node v hears a message from a neighbor w in a given round, if v listens in this round, and if w is its only neighbor that transmits in this round. If v listens in a round, and two or more neighbors of v transmit in this round, a collision occurs at v. If v transmits in a round, it does not hear anything in this round. Two scenarios are considered in the literature: if listening nodes can distinguish collision from silence (the latter occurs when no neighbor transmits), we say that the network has the collision detection capability, otherwise there is no collision detection. We consider the task of size discovery: finding the size of an unknown radio network with collision detection. All nodes have to output the size of the network, using a deterministic algorithm. Nodes have labels which are (not necessarily distinct) binary strings. The length of a labeling scheme is the largest length of a label. We concentrate on the following problem: What is the shortest labeling scheme that permits size discovery in all radio networks of maximum degree Δ? Our main result states that the minimum length of such a labeling scheme is Θ(loglogΔ). The upper bound is proven by designing a size discovery algorithm using a labeling scheme of length O (loglogΔ), for all networks of maximum degree Δ. The matching lower bound is proven by constructing a class of graphs (in fact even of trees) of maximum degree Δ, for which any size discovery algorithm must use a labeling scheme of length at least Ω(loglogΔ) on some graph of this class.

Deterministic Graph Exploration with Advice

We consider the task of graph exploration. An

Short Labeling Schemes for Topology Recognition in Wireless Tree Networks

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Generalized Bounded Tree Cover of a Graph

-node graph has unlabeled nodes, and all ports at any node of degree

Approximation Algorithms for Generalized Bounded Tree Cover

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POSTER: Approximation Algorithm for Minimizing the Size of Coverage Hole in Wireless Sensor Networks

are arbitrarily numbered