Connectivity in Multi-Radio, Multi-Channel Heterogeneous AD HOC Networks

Gossain, H.; Agrawal, Dharma

doi:10.1109/pimrc.2005.1651655

Cited by 18 publications

(18 citation statements)

References 19 publications

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“…Multi-interface wireless networks have been recently studied in a variety of contexts, usually focusing on the benefits of multiple radio devices of each node [10,15,16]. Many basic problems of standard wireless network optimization can be reconsidered in such a setting [4].…”

Section: Related Workmentioning

confidence: 99%

“…When k = 2, either there exists one common interface for all the nodes (code lines 1-2 of Algorithm 1), or the optimal solution costs 2 which implies to activate all the available interfaces at all the nodes (code lines [4][5]. Note that, in this case code lines [6][7][8][9][10] -8). In this way, all the edges connecting two nodes holding at most 2 interfaces and all the edges connecting a node holding 3 interfaces with a node holding at most 2 interfaces are covered.…”

Section: Theorem 2 In the Unit Cost Case Withmentioning

confidence: 99%

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Minimize the Maximum Duty in Multi-interface Networks

2011

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We consider devices equipped with multiple wired or wireless interfaces. By switching of various interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider two basic networking problems in the field of multi-interface networks. The first one, known as the Coverage problem, requires to establish the connections defined by a network. The second one, known as Connectivity problem, requires to guarantee a connecting path between any pair of nodes of a network. Both are subject to the constraint of keeping as low as possible the maximum cost set of active interfaces at each single node. We study the problems of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges in the first case, or to ensure connectivity in the second case. We prove that the Coverage problem is NP -hard for any fixed ∆ ≥ 5 and k ≥ 16, with ∆ being the maximum degree, and k being the number of different interfaces among the network. We also show that, unless P = NP, the problem cannot be approximated within a factor of η ln ∆, for a certain constant η. We then provide a general approximation algorithm which guarantees a factor of O((1 + b) ln ∆), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented. Concerning the Connectivity problem, we prove that it is NP -hard for any fixed ∆ ≥ 3 and k ≥ 10. Also for this problem, the inapproximability result holds, that is, unless P = NP, the problem cannot be approximated within a factor of η ln ∆, for a certain constant η. We then provide approximation and exact algorithms for the general problem and for special cases, respectively.

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Section: Related Workmentioning

confidence: 99%

Section: Theorem 2 In the Unit Cost Case Withmentioning

confidence: 99%

Minimize the Maximum Duty in Multi-interface Networks

2011

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“…Many basic problems of standard wireless network optimisation can be reconsidered in such a setting [1], focusing in particular on issues related to routing [8] and network connectivity [6,9].…”

Section: Related Workmentioning

confidence: 99%

Exploiting multi-interface networks: Connectivity and Cheapest Paths

2009

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Abstract. Let G = (V, E) be a graph which models a set of wireless devices (nodes V ) that can communicate by means of multiple radio interfaces, according to proximity and common interfaces (edges E). The problem of switching on (activating) the minimum cost set of interfaces at the nodes in order to guarantee the coverage of G was recently studied. A connection is covered (activated) when the endpoints of the corresponding edge share at least one active interface. In general, every node holds a subset of all the possible k interfaces. Such networks are known as multi-interface networks. In this setting, we study two basic problems: Connectivity and Cheapest Path. The Connectivity problem corresponds to the well-known Minimum Spanning Tree problem in graph theory. In practice, we need to cover a subgraph of G of minimum cost which contains a spanning tree of G. The problem turns out to be APX -hard in general and for many restricted graph classes, however it is possible to provide approximation algorithms: a 2-approximation in general and a (2 − 1 k )-approximation for the unit cost interface case, i.e. when the cost of activating an interface is unitary for any interface. We also consider the problem in special graph classes, such as graphs of bounded degree, planar graphs, graphs of bounded treewidth, complete graphs. The Cheapest Path problem corresponds to the well-known Shortest Path problem in graph theory. In the multi-interface setting this problem is still polynomially solvable, and we point out a simple Dijsktra-based algorithm with O(k|E| + k|V | log(k + |V |)) runtime in general and O(k(|E| + |V |)) runtime for the unit cost interface case.

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“…Multi-interface wireless networks have recently been studied in a variety of contexts, usually focusing on the benefits of multiple radio devices of each node. Many basic problems of standard wireless network optimization can be reconsidered in such a setting [6], in particular, focusing on issues related to routing [12] and network connectivity [8,13]. The study of combinatorial problems on multi-interface wireless networks has originated from [7].…”

Section: Introductionmentioning

confidence: 99%

Maximum flow and minimum-cost flow in multi-interface networks

D’Angelo

Stefano

Navarra

2011

Proceedings of the 5th International Conference on Ubiquitous Information Management and Communication

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In heterogeneous networks, devices can communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost, and provides a communication bandwidth. In this paper, we consider two fundamental optimization problems. In the first one, we aim to activate a set of interfaces in the network G = (V, E) in order to guarantee the maximal bandwidth between two given nodes. Nodes V represent the devices, edges E represent the connections that can be established according to the availability of the interfaces in the devices. In the second problem, we look for activating the cheapest set of interfaces among a network in order to guarantee a minimum bandwidth B of communication between two specified nodes. We show that the first problem is polynomially solvable while the second one is NP -Hard. However, we experimentally analyzed an algorithm for the second problem, showing that in practical cases it guarantees a low approximation ratio which allows us to use it in real-world networks.

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Connectivity in Multi-Radio, Multi-Channel Heterogeneous AD HOC Networks

Cited by 18 publications

References 19 publications

Minimize the Maximum Duty in Multi-interface Networks

Minimize the Maximum Duty in Multi-interface Networks

Exploiting multi-interface networks: Connectivity and Cheapest Paths

Maximum flow and minimum-cost flow in multi-interface networks

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