Xujin Chen

Minimum data aggregation time problem in wireless sensor networks

Wireless sensor networks promise a new paradigm for gathering data via collaboration among sensors spreading over a large geometrical region. Many real-time applications impose stringent delay requirements and ask for time-efficient schedules of data aggregations in which sensed data at sensors are combined at intermediate sensors along the way towards the data sink. The Minimum Data Aggregation Time (MDAT) problem is to find the schedule that routes data appropriately and has the shortest time for all requested data to be aggregated to the data sink. In this paper we study the MDAT problem with uniform transmission range of all sensors. We assume that, in each time round, data sent by a sensor reaches exactly all sensors within its transmission range, and a sensor receives data if it is the only data that reaches the sensor in this time round. We first prove that this problem is NP-hard even when all sensors are deployed a grid and data on all sensors are required to be aggregated to the data sink. We then design a (Δ–1)-approximation algorithm for MDAT problem, where Δ equals the maximum number of sensors within the transmission range of any sensor. We also simulate the proposed algorithm and compare it with the existing algorithm. The obtained results show that our algorithm has much better performance in practice than the theoretically proved guarantee and outperforms other algorithm.

Approximation Algorithms for Soft-Capacitated Facility Location in Capacitated Network Design

Abstract Answering an open question published in Operations Research (54, 73–91, 2006) in the area of network design and logistic optimization, we present the first constant-factor approximation algorithms for the problem combining facility location and cable installation in which capacity constraints are imposed on both facilities and cables. We study the problem of designing a minimum cost network to serve client demands by opening facilities for service provision and installing cables for service shipment. Both facilities and cables have capacity constraints and incur buy-at-bulk costs. This Max SNP-hard problem arises in diverse applications and is shown in this paper to admit a combinatorial 19.84-approximation algorithm of cubic running time. This is achieved by an integration of primal-dual schema, Lagrangian relaxation, demand clustering and bi-factor approximation. Our techniques extend to several variants of this problem, which include those with unsplitable demands or requiring network connectivity, and provide constant-factor approximate algorithms in strongly polynomial time.

Data Gathering Schedule for Minimal Aggregation Time in Wireless Sensor Networks

Data aggregation promises a new paradigm for gathering data via collaboration among wireless sensors deployed over a large geographical region. Many real-time applications impose stringent delay requirements and ask for time-efficient schedules of data gathering in which data sensed at sensors are aggregated at intermediate sensors along the way towards the data sink. The Minimal Aggregation Time (MAT) problem is to find the schedule that routes data appropriately and has the shortest time for all requested data to be aggregated and sent to the data sink. In this article we consider the MAT problem with collision-free transmission where a sensor can not receive any data if more than one sensors within its transmission range send data at the same time. We first prove that the MAT problem is NP-hard even if all sensors are deployed on a grid. We then propose a (Δ −1)-approximation algorithms for the MAT problem, where Δ is the maximum number of sensors within the transmission range of any sensor. By exploiting the geometric nature of wireless sensor networks, we obtain some better theoretical results for some special cases. We also simulate the proposed algorithm. The numerical results show that our algorithm has much better performance in practice than the theoretically proved guarantees and outperforms other existing algorithms.

Approximability of the Minimum Weighted Doubly Resolving Set Problem

Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by modeling it as the minimum weighted doubly resolving set problem, which is a strengthening of the well-known metric dimension problem.

The price of atomic selfish ring routing

We study selfish routing in ring networks with respect to minimizing the maximum latency. Our main result is an establishment of constant bounds on the price of stability (PoS) for routing unsplittable flows with linear latency. We show that the PoS is at most 6.83, which reduces to 4.57 when the linear latency functions are homogeneous. We also show the existence of a (54,1)-approximate Nash equilibrium. Additionally we address some algorithmic issues for computing an approximate Nash equilibrium.

Inapproximability and approximability of maximal tree routing and coloring

Let G be a undirected connected graph. Given g groups each being a subset of V(G) and a number of colors, we consider how to find a subgroup of subsets such that there exists a tree interconnecting all vertices in each subset and all trees can be colored properly with given colors (no two trees sharing a common edge receive the same color); the objective is to maximize the number of subsets in the subgroup. This problem arises from the application of multicast communication in all optical networks. In this paper, we first obtain an explicit lower bound on the approximability of this problem and prove Ω(g1−ε)-inapproximability even when G is a mesh. We then propose a simple greedy algorithm that achieves performance ratio O√|E(G)|, which matches the theoretical bounds.

A polynomial solvable minimum risk spanning tree problem with interval data

We propose and study a new model for the spanning tree problem with interval data, the Minimum Risk Spanning Tree (MRST) problem, that finds diverse applications in network design. Given an underlying network G=(V,E), each link e[set membership, variant]E can be established by paying a cost , and accordingly takes a risk of link failure. The MRST problem is to establish a spanning tree T in G of total cost not more than a given constant so that the risk sum over the links in T is minimized. We prove that the MRST problem can be solved in polynomial time, and thus has algorithmic aspect more satisfactory than the NP-hard robust spanning tree problem with interval data.

A Min-Max Theorem on Tournaments

We present a structural characterization of all tournaments

Excluding Braess’s Paradox in Nonatomic Selfish Routing

T=(V,A)

Copula-Based Randomized Mechanisms for Truthful Scheduling on Two Unrelated Machines

such that, for any nonnegative integral weight function defined on