Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is a optimization problem in the nondeterministic polynomial-complete complexity class, therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Er\"odos-Renyi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.Comment: 6 page

Design and Implementation of a Wireless Sensor Network for Smart Homes

Wireless sensor networks (WSNs) have become indispensable to the realization of smart homes. The objective of this paper is to develop such a WSN that can be used to construct smart home systems. The focus is on the design and implementation of the wireless sensor node and the coordinator based on ZigBee technology. A monitoring system is built by taking advantage of the GPRS network. To support multi-hop communications, an improved routing algorithm based on the Dijkstra algorithm is presented. Preliminary simulations have been conducted to evaluate the performance of the algorithm.Comment: International Workshop on Mobile Cyber-Physical Systems (MobiCPS 2010), in conjunction with UIC2010, IEEE, Xi'an, China, 26 - 29 October, 201

Gravito-Electromagnetic Perturbations and QNMs of Regular Black Holes

In the framework of Einstein's gravity coupled to nonlinear electromagnetic fields, we study gravito-electromagnetic perturbations of magnetic regular black holes. The master equations of perturbations are obtained through Chandrasekhar's procedure, in which gravitational perturbations with odd-parity are coupled to the electromagnetic perturbations with even-parity. As an application, we apply the master equations to obtain quasinormal modes (QNMs) for three types of regular black holes by using numerical method. Results show that QNMs of regular black holes depends significantly on the parameters of the theory and the magnetic charge of the black holes and are very different from that of the Reissner-Nordstr\"om black hole. Indications of these results on the stability of these regular black holes are discussed in detail.Comment: 21 pages, 2 figures, 3 tables, references adde