Yuzhuang Hu

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.

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.

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.

Approximation Algorithms for the Multi-Vehicle Scheduling Problem

In this paper we investigate approximation algorithms for the multi-vehicle scheduling problem (MVSP). In MVSP we are given a graph G = (V,E), where each vertex u of V is associated with a job j(u), and each edge e has a non-negative weight w(e). There are m identical vehicles available to service the jobs. Each job j(u) has its own release time r(u) and handling time h(u). A job j(u) can only be serviced by one vehicle after its release time r(u), and the handling time h(u) represents the time needed to finish processing j(u). The objective is to find a schedule in which the maximum completion time of the jobs, i.e. the makespan, is minimized. In this paper we present a 3-approximation algorithm for MVSP on trees, and a (\(5-\frac{2}{m}\))-approximation algorithm for MVSP on general graphs.

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.

Approximation algorithms for the black and white traveling salesman problem

The black and white traveling salesman problem (BWTSP) is to find the minimum cost hamiltonian tour of an undirected complete graph G, containing black and white vertices, subject to two restrictions: the number of white vertices, and the cost of the subtour between two consecutive black vertices are bounded. This paper focuses on designing approximation algorithms for the BWTSP in a graph satisfying the triangle inequality. We show that approximating the tour which satisfies the length constraint is NP-hard. We then show that the BWTSP can be approximated with tour cost (4 - 3/2Q) times the optimal cost, when at most Q white vertices appear between two consecutive black vertices. When exactly Q white vertices appear between two consecutive black vertices, the approximation bound can be slightly improved to (4- 15/8Q). This approximation bound is further improved to 2.5 when Q = 2.

k-delivery traveling salesman problem on tree networks.

In this paper we study the k-delivery traveling salesman problem (TSP)on trees, a variant of the non-preemptive capacitated vehicle routing problem with pickups and deliveries. We are given n pickup locations and n delivery locations on trees, with exactly one item at each pickup location. The k-delivery TSP is to find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each delivery location. We show that an optimal solution for the k-delivery TSP on paths can be found that allows succinct representations of the routes. By exploring the symmetry inherent in the k-delivery TSP, we design a 5/3-approximation algorithm for the k-delivery TSP on trees of arbitrary heights. The ratio can be improved to (3/2 - 1/2k) for the problem on trees of height 2. The developed algorithms are based on the following observation: under certain conditions, it makes sense for a non-empty vehicle to turn around and pick up additional loads.

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].

Efficient algorithms for the conditional covering problem

We consider the conditional covering problem in an undirected network, in which each vertex represents a demand point that must be covered by a facility as well as a potential facility site. Each facility can cover all vertices within a given coverage radius, except the vertex at which the facility is located. The objective is to locate facilities to cover all vertices such that the total facility location cost is minimized. In this paper, new upper bounds are proposed for the conditional covering problem on paths, cycles, extended stars, and trees. In particular, we provide an O(nlogn)-time algorithm for paths, an O(n^2logn)-time algorithm for cycles, an O(n^1^.^5logn)-time algorithm for extended stars, and an O(n^3)-time algorithm for trees. Our algorithms for paths, extended stars, and trees improve the previous upper bounds from O(n^2), O(n^2), and O(n^4), respectively.

Approximation Algorithms for a Network Design Problem

A class of network design problems, including the k -path/ tree/cycle covering problems and some location-routing problems, can be modeled by downwards monotone functions [5]. We consider a class of network design problems, called the p -constrained path/tree/cycle covering problems, obtained by introducing an additional constraint to these problems; i.e., we require that the number of connected components in the optimal solution be at most p for some integer p . The p -constrained path/tree/cycle covering problems cannot be modeled by downwards monotone functions. In this paper, we present a different analysis for the performance guarantee of the algorithm in [5]. As a result of the analysis, we are able to tackle p -constrained path/tree/cycle covering problems, and show the performance bounds of 2 and 4 for p -constrained tree/cycle problems and p -constrained path covering problems respectively.