Local Algorithms for Dominating and Connected Dominating Sets of Unit Disk Graphs with Location Aware Nodes

Czyzowicz, Jurek; Dobrev, Štefan; Fevens, Thomas; González-Aguilar, Hernàn; Kranakis, Evangelos; Opatrný, Jaroslav; Urrutia, Jorge

doi:10.1007/978-3-540-78773-0_14

Cited by 19 publications

(20 citation statements)

References 26 publications

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“…Experimental results show that this algorithm outperforms all existing distributed algorithms in terms of the size of the constructed CDS with a complexity comparable to its most efficient competitors. We also present a local implementation of this algorithm using the tiling scheme first proposed in [6]. The performance of the local algorithm is also comparable with the best algorithm in this category presented in [9].…”

Section: Introductionmentioning

confidence: 59%

Efficient Algorithms for Connected Dominating Sets in Ad Hoc Networks

Kassaei

Mehrandish

Narayanan

et al. 2010

2010 IEEE Wireless Communication and Networking Conference

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A Connected Dominating Set (CDS) can be used as a routing backbone in ad hoc networks and a data gathering/dissemination infrastructure in sensor networks. This virtual backbone can efficiently narrow down the search space for a route to the nodes in the CDS and thus be used by any routing protocol. Ideally, the backbone should constitute the smallest percentage of nodes in the network. However, finding a Minimum CDS (MCDS) is an NP-hard problem. In this paper, we propose an efficient distributed algorithm to construct a CDS in general graphs. The time and message complexity of our algorithm is linear in the number of nodes and degree of the network. Extensive simulations on Unit Disk Graphs (UDGs) show that this algorithm outperforms the distributed algorithms proposed in [3], [8], [11], and [14]in terms of the size of the CDS. We also present a local implementation of our algorithm in location-aware UDGs. Our algorithm provides the flexibility to arbitrarily adjust the tradeoff between the degree of locality and the size of the generated CDS.

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Section: Introductionmentioning

confidence: 59%

Efficient Algorithms for Connected Dominating Sets in Ad Hoc Networks

Kassaei

Mehrandish

Narayanan

et al. 2010

2010 IEEE Wireless Communication and Networking Conference

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“…As have been already stated above, in the general case, Kuhn et al [19] provide a negative answer and state that at least Ω( log n/ log log n) communication rounds are needed. Along with that, in several other related communication models, such as the unit disc graph, local approximation algorithms are known to exist [6]. In this paper, we show that any deterministic algorithm with a nontrivial approximation ratio requires at least Ω(log * n) rounds, thus answering negatively to the question stated above.…”

Section: Introductionmentioning

confidence: 88%

“…Although the dominating set problem remains NP-hard in this model, approximation algorithms with a constant ratio are known (e.g., [6,20]). Recently, Lenzen and Wattenhofer [22] showed that any f -approximation algorithm for the dominating set problem in the UDG model runs in g(n) time, where f (n)g(n) ∈ Ω(log * n).…”

Section: Related Workmentioning

confidence: 99%

Deterministic Dominating Set Construction in Networks with Bounded Degree

Friedman

Kogan

2011

Distributed Computing and Networking

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Abstract. This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usually significantly smaller than n, the total number of nodes in the system. Such networks arise in various settings of wireless and peer-to-peer communication. A trivial approach of choosing all nodes into the dominating set yields an algorithm with the approximation ratio of Δ + 1. We show that any deterministic algorithm with non-trivial approximation ratio requires Ω(log * n) rounds, meaning effectively that no o(Δ)-approximation deterministic algorithm with a running time independent of the size of the system may ever exist. On the positive side, we show two deterministic algorithms that achieve log Δ and 2 log Δ-approximation in O(Δ 3 + log * n) and O(Δ 2 log Δ + log * n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.

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“…Indeed, quite a few local algorithms are known for location-aware graphs [6,[10][11][12]19,20,23,[25][26][27]30,48,51,52,[54][55][56][57][58][59]. In this work, we give a unified description and analysis of a class of local algorithms based on a simple ''tile-and-combine'' idea: decompose the plane into tiles, have each tile solve its subproblem optimally, and combine the solutions into a global output.…”

Section: Introductionmentioning

confidence: 99%

Analysing local algorithms in location-aware quasi-unit-disk graphs

Hassinen

Kaasinen

Kranakis

et al. 2011

Discrete Applied Mathematics

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a b s t r a c tA local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node.We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set.We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

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Local Algorithms for Dominating and Connected Dominating Sets of Unit Disk Graphs with Location Aware Nodes

Cited by 19 publications

References 26 publications

Efficient Algorithms for Connected Dominating Sets in Ad Hoc Networks

Efficient Algorithms for Connected Dominating Sets in Ad Hoc Networks

Deterministic Dominating Set Construction in Networks with Bounded Degree

Analysing local algorithms in location-aware quasi-unit-disk graphs

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