Tight Bounds for MIS in Multichannel Radio Networks

Daum et al. [PODC'13] presented an algorithm that computes a maximal independent set (MIS) within $O(\log^2 n/F+\log n \mathrm{polyloglog} n)$ rounds in an $n$-node multichannel radio network with $F$ communication channels. The paper uses a multichannel variant of the standard graph-based radio network model without collision detection and it assumes that the network graph is a polynomially bounded independence graph (BIG), a natural combinatorial generalization of well-known geographic families. The upper bound of that paper is known to be optimal up to a polyloglog factor. In this paper, we adapt algorithm and analysis to improve the result in two ways. Mainly, we get rid of the polyloglog factor in the runtime and we thus obtain an asymptotically optimal multichannel radio network MIS algorithm. In addition, our new analysis allows to generalize the class of graphs from those with polynomially bounded local independence to graphs where the local independence is bounded by an arbitrary function of the neighborhood radius.Comment: 37 pages, to be published in DISC 201

Cell Size in Hybrid Wireless Systems

In this paper we study, analytically and via simulation, the impact ofreducing the cell size of a wireless system on the system capacity andhand-off failure rate. First, we focus on a pure cellular system. Wedevelop exact and approximate models for cellular systems in order toemphasize the blocking probability/forced termination probabilitytrade-off. This trade-off motivates the problem of optimizing the systemperformance with respect to the cell size. For hybrid systems, weinvestigate how jointly optimizing the number of cells per spot-beam, andthe bandwidth partitioning could improve the QoS parameters of interest.For both systems, the numerical solution is only feasible for smallnumber of cells. For large systems, a simulation study is presented.<P

Optimization of Connection-Oriented, Mobile, Hybrid Network Systems

In this paper we consider the extension of a cellular system by means of satellite channels. Specifically, we consider an area covered by a number of cells that is also covered by a number of spot-beams. We consider connection-oriented service and call durations are assumed to be exponentially distributed. Also, users are mobile and, as such, they may cross cell and/or spot- beam boundaries, thus necessitating hand-offs. We incorporate the possibility of call-dropping due to unsuccessful hand-off attempts, in addition to satellite propagation delays along with the probability of new call blocking and formulate a specific cost function that must be ultimately minimized. The minimization is to be carried out by choosing (1) the optimal split of the total number of channels between the cellular and the satellite systems, and (2) the call admission and assignment policy, subject to the constraints of a demand vector that consists of an exogenous (new-call) generation process and an internal (hand- off-based) process that results from the mobility model. This complex optimization problem is solved by means of both numerical and standard clock simulation techniques along with the ordinal optimization approach. This paper was presented at the "17th AIAA International Communications Satellite Systems Conference and Exhibit", February 24-26, 1998, Yokohama, Japan

Using Battery Level as Metric for Graph Planarization

International audienceTopology control in wireless sensor networks is an important issue for scalability and energy efficiency. It is often based on graph reduction performed through the use of Gabriel Graph or Relative Neighborhood Graph. This graph reduction is usually based on geometric values. In this paper we tackle the problem of possible connectivity loss in the reduced graph by applying a battery level based reduction graph. Experiments are conducted to evaluate our proposition. Results are compared with RNG reduction which takes into account only the strength of the received signal (RSSI). Results show that our algorithm maintains network connectivity longer than solutions from the literature and balances the energy consumption over nodes

Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Measurement-Adaptive Cellular Random Access Protocols

This work considers a single-cell random access channel (RACH) in cellular wireless networks. Communications over RACH take place when users try to connect to a base station during a handover or when establishing a new connection. Within the framework of Self-Organizing Networks (SONs), the system should self- adapt to dynamically changing environments (channel fading, mobility, etc.) without human intervention. For the performance improvement of the RACH procedure, we aim here at maximizing throughput or alternatively minimizing the user dropping rate. In the context of SON, we propose protocols which exploit information from measurements and user reports in order to estimate current values of the system unknowns and broadcast global action-related values to all users. The protocols suggest an optimal pair of user actions (transmission power and back-off probability) found by minimizing the drift of a certain function. Numerical results illustrate considerable benefits of the dropping rate, at a very low or even zero cost in power expenditure and delay, as well as the fast adaptability of the protocols to environment changes. Although the proposed protocol is designed to minimize primarily the amount of discarded users per cell, our framework allows for other variations (power or delay minimization) as well.Comment: 31 pages, 13 figures, 3 tables. Springer Wireless Networks 201

Perfect periodic scheduling for binary tree routing in wireless networks

In this paper we tackle the problem of coordinating transmission of data across a Wireless Mesh Network. The single task nature of mesh nodes imposes simultaneous activation of adjacent nodes during transmission. This makes the coordinated scheduling of local mesh node traffic with forwarded traffic across the access network to the Internet via the Gateway notoriously difficult. Moreover, with packet data the nature of the coordinated transmission schedule has a big impact upon both the data throughput and energy consumption. Perfect Periodic Scheduling, in which each demand is itself serviced periodically, provides a robust solution. In this paper we explore the properties of Perfect Periodic Schedules with modulo arithmetic using the Chinese Remainder Theorem. We provide a polynomial time, optimisation algorithm, when the access network routing tree has a chain or binary tree structure. Results demonstrate that energy savings and high throughput can be achieved simultaneously. The methodology is generalisable

Average flow constraints and stabilizability in uncertain production-distribution systems

We consider a multi-inventory system with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first-order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of two requirements: (i) meeting any possible demand at each time (worst case stability) or (ii) achieving a predefined flow in the average (average flow constraints). Necessary and sufficient conditions for the achievement of both goals have been proposed by the authors. In this paper, we face the case in which these conditions are not satisfied. We show that, if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case, we provide a tight bound for the cost