Train Scheduling on a Unidirectional Path

We formulate what might be the simplest train scheduling problem considered in the literature and show it to be NP-hard. We also give a log-factor randomised algorithm for it. In our problem we have a unidirectional train track with equidistant stations, each station initially having at most one train. In addition, there can be at most one train poised to enter each station. The trains must move to their destinations subject to the constraint that at every time instant there can be at most one train at each station and on the track between stations. The goal is to minimise the maximum delay of any train. Our problem can also be interpreted as a packet routing problem, and our work strengthens the hardness results from that literature

Willage: A Two-Tiered Peer-to-Peer Resource Sharing Platform for Wireless Mesh Community Networks

The success of experiences such as Seattle and Houston Wireless has attracted the attention on the so called wireless mesh community networks. These are wireless multihop networks spontaneously deployed by users willing to share communication resources. Due to the community spirit characterizing such networks, it is likely that users will be willing to share other resources besides communication resources, such as data, images, music, movies, disk quotas for distributed backup, and so on. In other words, it is expected that peer-to-peer applications will be deployed in such type of networks. In this paper we propose Willage, a platform for resource localization in wireless mesh community networks with mobile users. The platform is based on a two-tiered architecture: resources are made available at the lower tier, which is composed of mobile terminals, whereas information on their localization is managed at the upper layer, which is composed of wireless mesh routers. We also introduce Georoy, an algorithm for the efficient retrieval of the information on resource localization based on the Viceroy algorithm. Simulation results show that Willage achieves its goal of enabling efficient and scalable peer-to-peer resource sharing in wireless mesh community networks

Geometric Spanner of Segments (Algorithms and Computation)

Algorithms and computation : 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007 : proceedings ; ISAAC 2007 : (Lecture notes in computer science ; 4835)Proc. of ISACCGeometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider a generalization of the classical geometric spanner problem (called segment spanner): Given a set S of disjoint 2-D segments, find a spanning network G with minimum size so that for any pair of points in S, there exists a path in G with length no more than t times their Euclidean distance. Based on a number of interesting techniques (such as weakly dominating set, strongly dominating set, and interval cover), we present an efficient algorithm to construct the segment spanner. Our approach first identifies a set of Steiner points in S, then construct a point spanner for them. Our algorithm runs in O(|Q| + n 2 logn) time, where Q is the set of Steiner points. We show that Q is an O(1)-approximation in terms of its size when S is relatively “well” separated by a constant. For arbitrary rectilinear segments under L 1 distance, the approximation ratio improves to 2

Universal packet routing with arbitrary bandwidths and transit times

A fundamental problem in communication networks is store-and-forward packet routing. In a celebrated paper Leighton, Maggs, and Rao proved that the length of an optimal schedule is linear in the trivial lower bounds congestion and dilation. However, there has been no improvement on the actual bounds in more than 10 years. Also, commonly the problem is studied only in the setting of unit bandwidths and unit transit times. In this paper, we prove bounds on the length of optimal schedules for packet routing in the setting of arbitrary bandwidths and arbitrary transit times. Our results generalize the existing work to a much broader class of instances and also improve the known bounds significantly. For the case of unit transit times and bandwidths, we improve the best known bound of 39(C+D) to 23.4(C+D), where C and D denote the congestion and dilation, respectively. If every link in the network has a certain minimum transit time or capacity we improve this bounds to up to 4.25(C+D). Key to our results is a framework which employs tight bounds for instances where each packet travels along only a small number of edges. Further insights for such instances would reduce our constants even more

Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme crn achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for finding an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmics, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

Efficient Data Dissemination in Wireless Ad Hoc Networks

In this thesis, we study the problem of efficient data dissemination in wireless sensor and mobile ad hoc networks. In wireless sensor networks we study two problems: (1) construction of virtual backbones and clustering hierarchies to achieve efficient routing, and (2) placement of multiple sinks, where each sensor is at a bounded distance to several sinks, to analyze and process data before sending it to a central unit. Often connected dominating sets have been used for such purposes. However, a connected dominating set is often vulnerable due to frequent node failures in wireless sensor networks. Hence, to provide a degree of fault-tolerance we consider in problem (1) a 2-connected (k,r)-dominating set, denoted D(2,k,r), to act as a virtual backbone or a clustering hierarchy, and in problem (2) a total (k,r)-dominating set to act as sinks in wireless sensor networks. Ideally, the backbone or the number of sinks in the network should constitute the smallest percentage of nodes in the network. We model the wireless sensor network as a graph. The total (k,r)-dominating set and the 2-connected (k,r)-dominating set have not been studied in the literature. Thus, we propose two centralized approximation algorithms to construct a D(2,k,r) in unit disk graphs and in general graphs. We also derive upper bounds on the total (k,r)-domination number in graphs of girth at least 2k+1 as well as in random graphs with non-fixed probability p. In mobile ad hoc networks we propose a hexagonal based beacon-less flooding algorithm, HBLF, to efficiently flood the network. We give sufficient condition that even in the presence of holes in the network, HBLF achieves full delivery. Lower and upper bounds are given on the number of forwarding nodes returned by HBLF in a network with or without holes. When there are no holes in the network, we show that the ratio of the shortest path returned by HBLF to the shortest path in the network is constant. We also present upper bounds on the broadcast time of HBLF in a network with or without holes

Topology control and data handling in wireless sensor networks

Our work in this thesis have provided two distinctive contributions to WSNs in the areas of data handling and topology control. In the area of data handling, we have demonstrated a solution to improve the power efficiency whilst preserving the important data features by data compression and the use of an adaptive sampling strategy, which are applicable to the specific application for oceanography monitoring required by the SECOAS project. Our work on oceanographic data analysis is important for the understanding of the data we are dealing with, such that suitable strategies can be deployed and system performance can be analysed. The Basic Adaptive Sampling Scheduler (BASS) algorithm uses the statistics of the data to adjust the sampling behaviour in a sensor node according to the environment in order to conserve energy and minimise detection delay. The motivation of topology control (TC) is to maintain the connectivity of the network, to reduce node degree to ease congestion in a collision-based medium access scheme; and to reduce power consumption in the sensor nodes. We have developed an algorithm Subgraph Topology Control (STC) that is distributed and does not require additional equipment to be implemented on the SECOAS nodes. STC uses a metric called subgraph number, which measures the 2-hops connectivity in the neighbourhood of a node. It is found that STC consistently forms topologies that have lower node degrees and higher probabilities of connectivity, as compared to k-Neighbours, an alternative algorithm that does not rely on special hardware on sensor node. Moreover, STC also gives better results in terms of the minimum degree in the network, which implies that the network structure is more robust to a single point of failure. As STC is an iterative algorithm, it is very scalable and adaptive and is well suited for the SECOAS applications