On the complexity of bandwidth allocation in radio networks

Klasing, Ralf; Morales, Nelson; Pérennès, Stéphane

doi:10.1016/j.tcs.2008.06.048

Cited by 31 publications

(44 citation statements)

References 22 publications

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“…It is important to know what are the sets of transmission links that can be active at the same time, the rounds. The Round Weighting Problem RWP was introduced in [2]. The authors make a primal/dual analysis and propose approximation algorithms for some specific network topologies.…”

Section: Related Workmentioning

confidence: 99%

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Bottleneck Analysis for Routing and Call Scheduling in Multi-Hop Wireless Networks

Gomes

Pérennès

Rivano

2008

2008 IEEE Globecom Workshops

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Abstract-In this paper, we address the routing and call scheduling problem in which one has to find a minimum-length schedule of selected links in a TDMA (Time Division Multiple Access) based wireless network. As we deal with multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. We present a cross-layer formulation of the problem that computes joint routing and scheduling.We use a branch-and-price algorithm to solve optimally the problem. A column generation algorithm is used to cope with the exponential set of rounds. The branch-and-bound algorithm provides mono-routing. We run experiments on networks from the literature, with different number of gateways. Experimental results as well as theoretical insights let us conjecture that the bottleneck region analysis is enough to find the optimal solution. The Integer Round-Up Property (IRUP) seems to hold for our problem. I. INTRODUCTIONIn wireless networks, the communication channels are shared among the terminals. Thus, one of the major problems faced is the reduction of capacity due to interferences caused by simultaneous transmissions [1]. In this work, we call a round a collection of links that can be simultaneously activated in the network. We address the problem called Round Weighting Problem (RWP) [2] that consider joint routing and scheduling. We present a cross-layer formulation of the problem. We have to find a minimum-length schedule of selected links in a TDMA (Time Division Multiple Access) based wireless network. As we deal with multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. Scheduling methods such TDMA can guarantee achieving higher capacities by allowing time slots to be shared by simultaneous transmissions.A communication graph G = (V, E) represents the network topology, where the nodes are the routers and the edges are the links. Interferences between links are given as a conflict graph G c . We consider the RWP as a flow routing problem. Therefore, the flows in the edges of the problem solution represent the allocated bandwidth.We work with a special case of RW P where data are exchanged only between the routers in V r and the gateways in V g such as in Wireless Mesh networks (WMNs) or sensor networks. The input of the RW P corresponds to the communication graph G(V r ∪ V g , E), the conflict graph G c representing the edge interferences, and the network bandwidth b v

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Section: Related Workmentioning

confidence: 99%

“…In this work, we call a round a collection of links that can be simultaneously activated in the network. We address the problem called Round Weighting Problem (RWP) [2] that consider joint routing and scheduling. We present a cross-layer formulation of the problem.…”

Section: Introductionmentioning

confidence: 99%

Bottleneck Analysis for Routing and Call Scheduling in Multi-Hop Wireless Networks

Gomes

Pérennès

Rivano

2008

2008 IEEE Globecom Workshops

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“…It is also shown that the problem of finding an optimal gathering algorithm (one that uses a minimum number of rounds) does not admit a Fully Polynomial Time Approximation Scheme if d I > d T , unless P=NP, and is NP-hard if d I = d T . Another related model can be found in [9], where the authors study the case in which steady-state flow demands between each pair of nodes have to be satisfied.…”

Section: Related Workmentioning

confidence: 99%

Gathering Algorithms on Paths Under Interference Constraints

Bermond

Corrêa

2006

Lecture Notes in Computer Science

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Abstract. We study the problem of gathering information from the nodes of a multi-hop radio network into a pre-determined destination node under interference constraints which are modeled by an integer d ≥ 1, so that any node within distance d of a sender cannot receive calls from any other sender. A set of calls which do not interfere with each other is referred to as a round. We give algorithms and lower bounds on the minimum number of rounds for this problem, when the network is a path and the destination node is either at one end or at the center of the path. The algorithms are shown to be optimal for any d in the first case, and for 1 ≤ d ≤ 4, in the second case.

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“…In order to ensure the largest stability region of the system we want to choose links so that the sum of their weight (queue-length) is as large as possible so as to realize a maximum matching. The idea behind the maximum matching is to decrease the largest queues.Centralized algorithms have been proposed to solve this problem both for random arrivals in [7] and deterministic arrivals in [6]. 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).…”

mentioning

confidence: 99%

“…Centralized algorithms have been proposed to solve this problem both for random arrivals in [7] and deterministic arrivals in [6]. 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).…”

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confidence: 99%

A distributed scheduling algorithm for wireless networks with constant overhead and arbitrary binary interference

Bermond

Mazauric

Misra

et al. 2010

SIGMETRICS Perform. Eval. Rev.

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This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, "neighboring links" cannot be simultaneously activated, otherwise transmissions will fail. Hereafter, we consider any binary model of interference. We follow the model described by Bui, Sanghavi, and Srikant in [3]. We assume. There are two phases during each slot: first the control phase which determines what links will be activated next, followed by a transmission phase during which data is transmitted. We assume random arrivals of data (packets) on each link during each slot, so that a buffer (queue) is associated to each link. It takes exactly one time slot to transmit a packet on a link. Since nodes do not have a global knowledge of the network, our aim (like in [3]) is to design for the control phase a distributed algorithm which identifies a set of non-interfering links.For example, in the primary node interference model (where two links interfere only if they are incident), a set of non interfering edges is called a matching. In order to ensure the largest stability region of the system we want to choose links so that the sum of their weight (queue-length) is as large as possible so as to realize a maximum matching. The idea behind the maximum matching is to decrease the largest queues.Centralized algorithms have been proposed to solve this problem both for random arrivals in [7] and deterministic arrivals in [6]. 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 work 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 of the queue-lengths) and it requires no knowledge. Indeed the algorithm in [5] does not have a constant overhead, whereas the one described in [3] is only valid for the primary node interference model. Furthermore, both algorithm need to know the queue lengths of the "neighboring links", which are difficult to obtain in a wireless network with interference. We prove that our algorithm gives a maximal set of active links (i.e. 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.Let us sketch the main ideas of our algorithm Algorithm Log. Details, proofs and examples can be found in the full version [1].We use a binary symmetric interference model and define the Copyright is held by the author/owner(s). ACM X-XXXXX-XX-X/XX/XX.interference set of a link e ∈ E, denoted by ε(e), as the set of edges interfering with e. We denote by c(e), the capacity of the edge e, that is the number of packets that e can serve during one time slot if the link e is active. Let qt(e) (al...

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On the complexity of bandwidth allocation in radio networks

Cited by 31 publications

References 22 publications

Bottleneck Analysis for Routing and Call Scheduling in Multi-Hop Wireless Networks

Bottleneck Analysis for Routing and Call Scheduling in Multi-Hop Wireless Networks

Gathering Algorithms on Paths Under Interference Constraints

A distributed scheduling algorithm for wireless networks with constant overhead and arbitrary binary interference

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