Qiaosheng Shi

Optimal movement of mobile sensors for barrier coverage of a planar region

Intrusion detection, area coverage and border surveillance are important applications of wireless sensor networks today. They can be (and are being) used to monitor large unprotected areas so as to detect intruders as they cross a border or as they penetrate a protected area. We consider the problem of how to optimally move mobile sensors to the fence (perimeter) of a region delimited by a simple polygon in order to detect intruders from either entering its interior or exiting from it. We discuss several related issues and problems, propose two models, provide algorithms and analyze their optimal mobility behavior.

Efficient algorithms for center problems in cactus networks

Efficient algorithms for solving the center problems in weighted cactus networks are presented. In particular, we have proposed the following algorithms for the weighted cactus networks of size n: an O(nlogn) time algorithm to solve the 1-center problem, and an O(nlog^3n) time algorithm to solve the weighted continuous 2-center problem. We have also provided improved solutions to the general p-center problems in cactus networks. The developed ideas are then applied to solve the obnoxious 1-center problem in weighted cactus networks.

Optimal Movement of Mobile Sensors for Barrier Coverage of a Planar Region

Intrusion detection, area coverage and border surveillance are important applications of wireless sensor networks today. They can be (and are being) used to monitor large unprotected areas so as to detect intruders as they cross a border or as they penetrate a protected area. We consider the problem of how to optimally move mobile sensors to the fence (perimeter) of a region delimited by a simple polygon in order to detect intruders from either entering its interior or exiting from it. We discuss several related issues and problems, propose two models, provide algorithms and analyze their optimal mobility behavior.

Efficient algorithms for the weighted 2-center problem in a cactus graph

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n logn) time algorithm is proposed that finds the weighted 1-center in a cactus graph, where n is the number of vertices in the graph. For the weighted 2-center problem, an O(n log3n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log2n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log3n). This improves the previous result of O(cn) where c is the number of distinct vertex weights used in the graph [8]. In the worst case c is O(n).

Sensor network connectivity with multiple directional antennae of a given angular sum

We investigate the problem of converting sets of sensors into strongly connected networks of sensors using multiple directional antennae. Consider a set S of n points in the plane modeling sensors of an ad hoc network. Each sensor uses a fixed number, say 1 ≤ k ≤ 5, of directional antennae modeled as a circular sector with a given spread (or angle) and range (or radius). We give algorithms for orienting the antennae at each sensor so that the resulting directed graph induced by the directed antennae on the nodes is strongly connected. We also study trade-offs between the total angle spread and range for maintaining connectivity.

An optimal algorithm for the continuous/discrete weighted 2-center problem in trees

In this paper, an optimal algorithm to solve the continuous/discrete weighted 2-center problem is proposed. The method generalizes the “trimming” technique of Megiddo [5] in a nontrivial way. This result allows an improved O(n log n) time algorithm for the weighted 3-center and 4-center problems.

Optimal algorithms for the weighted p-center problems on the real line for small p

An optimal linear time algorithm for the unweighted p-center problems in trees has been known since 1991 [4]. No such worst-case linear time result is known for the weighted version of the p-center problems, even for a path graph. In this paper, for fixed p, we propose two lineartime algorithms for the weighted p-center problem for points on the real line, thereby partially resolving a long-standing open problem. One of our approaches generalizes the trimming technique of Megiddo [10], and the other one is based on the parametric pruning technique, introduced here. The proposed solutions make use of the solutions of another variant of the center problem called the conditional center location problem [13].

Single Vehicle Scheduling Problems on Path/Tree/Cycle Networks with Release and Handling Times

In this paper, we consider the single vehicle scheduling problem (SVSP) on networks. Each job, located at some node, has a release time and a handling time. The vehicle starts from a node (depot), processes all the jobs, and then returns back to the depot. The processing of a job cannot be started before its release time, and its handling time indicates the time needed to process the job. The objective is to find a routing schedule of the vehicle that minimizes the completion time. When the underlying network is a path, we provide a simple 3/2-approximation algorithm for SVSP where the depot is arbitrarily located on the path, and a 5/3-approximation algorithm for SVSP where the vehicles starting depot and the ending depot are not the same. For the case when the network is a tree network, we show that SVSP is polynomially approximable within 11/6 of optimal. All these results are improvements of the previous results [2,4]. The approximation ratio is improved when the tree network has constant number of leaf nodes. For cycle networks, we propose a 9/5-approximation algorithm and show that SVSP without handling times can be solved exactly in polynomial time. No such results on cycle networks were previously known.

New Upper Bounds on Continuous Tree Edge-Partition Problem

We consider continuous tree edge-partition problem on a edge-weighted tree network. A continuous p-edge-partition of a tree is to divide it into psubtrees by selecting p? 1 cut points along the edges of the underlying tree. The objective is to maximize (minimize) the minimum (maximum) length of the subtrees. We present an O(nlog2n)-time algorithm for the max-min problem which is based on parametric search technique [7] and an efficient solution to the ratio search problem. Similar algorithmic technique, when applied to the min-max problem, results in an O(nh T logn)-time algorithm where h T is the height of the underlying tree network. The previous results for both max-min and min-max problems are O(n2) [5].

Optimal algorithms for the path/tree-shaped facility location problems in trees

In this paper we consider the problem of locating a path-shaped or tree-shaped (extensive) facility in trees under the condition that existing facilities are already located. We introduce a parametric-pruning method to solve the conditional extensive weighted 1-center location problems in trees in linear time. This improves the recent results of O(n logn) by Tamir et al. [16].