Wireless Broadcast with Network Coding: A Connected Dominating Sets Approach

We study network coding for multi-hop wireless networks. We focus the case of broadcasting, where one source transmits information to all the nodes in the network. Our goal is energy-efficient broadcasting, in other words, to minimize the number of transmissions for broadcasting to the entire network. To achieve this goal, we propose a family of methods that combine the use of network coding and connected dominating sets. They consists in rate selections using connected dominated sets (RAUDS: Rate Adjustment Using Dominating Sets, and an generalized version, MARAUDS). The main insight behind these methods is that their use of connected dominating sets, allows near-optimality in the core of the network, while they efficiently handle borders and non-uniformity. The main contribution is a formal proof of the performance of these families of algorithms. One main result is the comparison of performance between routing and these methods (and in general, network coding)

Wireless Broadcast with Network Coding: Energy Efficiency, Optimality and Coding Gain in Lossless Wireless Networks

We consider broadcasting in multi-hop wireless networks, in which one source transmits information to all the nodes in the networks. We focus on energy efficiency, or minimizing the total number of transmissions. Our main result is the proof that, from the energy-efficiency perspective, network coding may essentially operate in an optimal way in the core of the network for uniform wireless networks in Euclidean spaces with idealized communication. In such networks, one corollary is that network coding is expected to outperform routing. We prove that the asymptotic network coding gain is comprised between 1.642 and 1.684 for networks of the plane, and comprised between 1.432 and 2.035 for networks in 3-dimensional space

hpDJ: An automated DJ with floorshow feedback

Many radio stations and nightclubs employ Disk-Jockeys (DJs) to provide a continuous uninterrupted stream or “mix” of dance music, built from a sequence of individual song-tracks. In the last decade, commercial pre-recorded compilation CDs of DJ mixes have become a growth market. DJs exercise skill in deciding an appropriate sequence of tracks and in mixing 'seamlessly' from one track to the next. Online access to large-scale archives of digitized music via automated music information retrieval systems offers users the possibility of discovering many songs they like, but the majority of consumers are unlikely to want to learn the DJ skills of sequencing and mixing. This paper describes hpDJ, an automatic method by which compilations of dance-music can be sequenced and seamlessly mixed by computer, with minimal user involvement. The user may specify a selection of tracks, and may give a qualitative indication of the type of mix required. The resultant mix can be presented as a continuous single digital audio file, whether for burning to CD, or for play-out from a personal playback device such as an iPod, or for play-out to rooms full of dancers in a nightclub. Results from an early version of this system have been tested on an audience of patrons in a London nightclub, with very favourable results. Subsequent to that experiment, we designed technologies which allow the hpDJ system to monitor the responses of crowds of dancers/listeners, so that hpDJ can dynamically react to those responses from the crowd. The initial intention was that hpDJ would monitor the crowd’s reaction to the song-track currently being played, and use that response to guide its selection of subsequent song-tracks tracks in the mix. In that version, it’s assumed that all the song-tracks existed in some archive or library of pre-recorded files. However, once reliable crowd-monitoring technology is available, it becomes possible to use the crowd-response data to dynamically “remix” existing song-tracks (i.e, alter the track in some way, tailoring it to the response of the crowd) and even to dynamically “compose” new song-tracks suited to that crowd. Thus, the music played by hpDJ to any particular crowd of listeners on any particular night becomes a direct function of that particular crowd’s particular responses on that particular night. On a different night, the same crowd of people might react in a different way, leading hpDJ to create different music. Thus, the music composed and played by hpDJ could be viewed as an “emergent” property of the dynamic interaction between the computer system and the crowd, and the crowd could then be viewed as having collectively collaborated on composing the music that was played on that night. This en masse collective composition raises some interesting legal issues regarding the ownership of the composition (i.e.: who, exactly, is the author of the work?), but revenue-generating businesses can nevertheless plausibly be built from such technologies

Asynchronous Local Construction of Bounded-Degree Network Topologies Using Only Neighborhood Information

We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be directly connected to any one of its neighbors and picks its connections according to a unique topology control algorithm that is available at every node. Given that each node knows only the indices (unique identification numbers) of its one- and two-hop neighbors, we identify an algorithm that preserves connectivity and can operate without the need of any synchronization among nodes. Moreover, the algorithm results in a sparse graph with at most $5n$ edges and a maximum node degree of $10$. Existing algorithms with the same promises further require neighbor distance and/or direction information at each node. We also evaluate the performance of our algorithm for random networks. In this case, our algorithm provides an asymptotically connected network with $n(1+o(1))$ edges with a degree less than or equal to $6$ for $1-o(1)$ fraction of the nodes. We also introduce another asynchronous connectivity-preserving algorithm that can provide an upper bound as well as a lower bound on node degrees.Comment: To appear in IEEE Transactions on Communication

Optimization in Geometric Graphs: Complexity and Approximation

We consider several related problems arising in geometric graphs. In particular, we investigate the computational complexity and approximability properties of several optimization problems in unit ball graphs and develop algorithms to find exact and approximate solutions. In addition, we establish complexity-based theoretical justifications for several greedy heuristics. Unit ball graphs, which are defined in the three dimensional Euclidian space, have several application areas such as computational geometry, facility location and, particularly, wireless communication networks. Efficient operation of wireless networks involves several decision problems that can be reduced to well known optimization problems in graph theory. For instance, the notion of a \virtual backbone" in a wire- less network is strongly related to a minimum connected dominating set in its graph theoretic representation. Motivated by the vastness of application areas, we study several problems including maximum independent set, minimum vertex coloring, minimum clique partition, max-cut and min-bisection. Although these problems have been widely studied in the context of unit disk graphs, which are the two dimensional version of unit ball graphs, there is no established result on the complexity and approximation status for some of them in unit ball graphs. Furthermore, unit ball graphs can provide a better representation of real networks since the nodes are deployed in the three dimensional space. We prove complexity results and propose solution procedures for several problems using geometrical properties of these graphs. We outline a matching-based branch and bound solution procedure for the maximum k-clique problem in unit disk graphs and demonstrate its effectiveness through computational tests. We propose using minimum bottleneck connected dominating set problem in order to determine the optimal transmission range of a wireless network that will ensure a certain size of "virtual backbone". We prove that this problem is NP-hard in general graphs but solvable in polynomial time in unit disk and unit ball graphs. We also demonstrate work on theoretical foundations for simple greedy heuristics. Particularly, similar to the notion of "best" approximation algorithms with respect to their approximation ratios, we prove that several simple greedy heuristics are "best" in the sense that it is NP-hard to recognize the gap between the greedy solution and the optimal solution. We show results for several well known problems such as maximum clique, maximum independent set, minimum vertex coloring and discuss extensions of these results to a more general class of problems. In addition, we propose a "worst-out" heuristic based on edge contractions for the max-cut problem and provide analytical and experimental comparisons with a well known "best-in" approach and its modified versions

Unifying information propagation models on networks and influence maximisation

Information propagation on networks is a central theme in social, behavioural, and economic sciences, with important theoretical and practical implications, such as the influence maximisation problem for viral marketing. Here, we consider a model that unifies the classical independent cascade models and the linear threshold models, and generalise them by considering continuous variables and allowing feedback in the dynamics. We then formulate its influence maximisation as a mixed integer nonlinear programming problem and adopt derivative-free methods. Furthermore, we show that the problem can be exactly solved in the special case of linear dynamics, where the selection criteria is closely related to the Katz centrality, and propose a customised direct search method with local convergence. We then demonstrate the close-to-optimal performance of the customised direct search numerically on both synthetic and real networks.Comment: 28 pages, 22 figure