Minimizing Flow Time in the Wireless Gathering Problem

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than \Omega(m^{1/3) when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to

A note on uniform power connectivity in the SINR model

In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or less colors, corresponding to the number of frequencies or time slots, are necessary. We consider the SINR model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise . The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent $\alpha$. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if $\alpha>1$ as well as in two-dimensional grids if $\alpha>2$. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of $\mathcal{O}(\log n)$ and $\Omega(\log n/\log\log n)$ for $\alpha=2$ and $\Theta(n^{2/\alpha-1})$ for $\alpha<2$ respectively. If nodes are distributed uniformly at random on the interval $[0,1]$, a \emph{regular} coloring of $\mathcal{O}(\log n)$ colors guarantees connectivity, while $\Omega(\log \log n)$ colors are required for any coloring.Comment: 13 page

Placement Optimal de points d'accès dans les réseaux radio maillés

National audienceCet article présente un modèle linéaire permettant de placer un nombre minimum de points d'accès dans un réseau radio maillé (Wireless Mesh Network). Connaissant la topologie du réseau, le problème est de déterminer le nombre minimum de points d'accès reliés à Internet nécessaires pour que la demande de chaque routeur soit satisfaite. Afin de prendre en compte les interférences spatiales dÛes a la technologie radio, le temps est découpé en intervalles réguliers au cours desquels un ensemble de liens n'interférant pas deux a deux est déterminé, ce qui engendre une limitation de la capacité des liens en fonction de leur activation dans le temps. Le placement se fait ensuite de manière à assurer à chaque noeud le débit désiré en régime permanent

Extracting algorithmic complexity in scientific literature for advance searching

Non-textual document elements such as charts, diagrams, algorithms and tables play an important role to present key information in scientific documents. Recent advances in information retrieval systems tap this information to answer more complex user queries by mining text pertaining to non-textual document elements from full text. Algorithms are critically important in computer science. Researchers are working on existing algorithms to improve them for critical application. Moreover, new algorithms for unsolved and newly faced problems are under development. These enhanced and new algorithms are mostly published in scholarly documents. The complexity of these algorithms is also discussed in the same document by the authors. Complexity of an algorithm is also an important factor for information retrieval (IR) systems. In this paper, we mine the relevant complexities of algorithms from full text document by comparing the metadata of the algorithm, such as caption and function name, with the context of the paragraph in which complexity related discussion is made by the authors. Using the dataset of 256 documents downloaded from CiteSeerX repository, we manually annotate 417 links between algorithms and their complexities. Further, we apply our novel rule-based approach that identifies the desired links with 81% precision, 75% recall, 78% F1-score and 65% accuracy. Overall, our method of identifying the links has potential to improve information retrieval systems that tap the advancements of full text and more specifically non-textual document elements

Distributed Call Scheduling in Wireless Networks

This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, "neighboring links'' cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We follow the model described by Bui, Sanghavi, and Srikant in SBS09,SBS07. We suppose that time is slotted and during each slot we have two phases: one control phase which determines what links will be activated and send data during the second phase. We assume random arrivals on each link during each slot, therefore a queue is associated to each link. Since nodes do not have a global knowledge of the network, our aim (like in SBS09,SBS07) is to design for the control phase, a distributed algorithm which determines a set of non interfering links. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this article we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues); and it needs no knowledge. Indeed contrary to other existing algorithms, we do not need to know the values of the queues of the "neighboring links'', which are difficult to obtain in a wireless network with interference. We prove that this algorithm gives a maximal set of active links (in each interference set, there is at least one active edge). We also give sufficient conditions for stability under Markovian assumptions. Finally the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes

Round weighting problem and gathering in radio networks with symmetrical interference

International audienceIn this article we consider the problem of gathering information in a gateway in a radio mesh access network. Due to interferences, calls (transmissions) cannot be performed simultaneously. This leads us to define a round as a set of non-interfering calls. Following the work of Klasing, Morales and Pérennes, we model the problem as a Round Weighting Problem (RWP) in which the objective is to minimize the overall period of non-interfering calls activations (total number of rounds) providing enough capacity to satisfy the throughput demand of the nodes.We develop tools to obtain lower and upper bounds for general graphs. Then, more precise results are obtained considering a symmetric interference model based on distance of graphs, called the distance-d interference model (the particular case d= 1 corresponds to the primary node model).We apply the presented tools to get lower bounds for grids with thegateway either in the middle or in the corner. We obtain upper boundswhich in most of the cases match the lower bounds, using strategiesthat either route the demand of a single node or route simultaneously flow from several source nodes. Therefore, weobtain exact and constructive results for grids, in particularfor the case of uniform demands answering a problem asked by Klasing, Morales and Pérennes

End-to-End Packet-Scheduling in Wireless Ad-hoc Networks

Abstract Packet-scheduling is a particular challenge in wireless networks due to interference from nearby transmissions. A distance-2 interference model serves as a useful abstraction here, and we study packet routing and scheduling under this model of interference. The main focus of our work is the development of fully-distributed (decentralized) protocols. We present polylogarithmic/constant factor approximation algorithms for various families of disk graphs (which capture the geometric nature of wireless-signal propagation), as well as near-optimal approximation algorithms for general graphs. A basic distributed coloring procedure, originally due to Luby (Journal of Computer and System Sciences, 47:250–286, 1993), underlies many of our algorithms. Experimental work of Finocchi, Panconesi, and Silvestri (SODA 2002) showed that a natural modification of this algorithm leads to improved performance, and a rigorous explanation of this was left as an open question; we prove that the modified algorithm is provably (much) better in the worst-case. Finally, using simulations, we study the impact of the routing strategy and the choice of parameters on the performance of our distributed algorithm for unit disk graphs.