Spanners and message distribution in networks

Farley, Arthur M.; Proskurowski, Andrzej; Zappala, Daniel; Windisch, Kurt

doi:10.1016/s0166-218x(03)00259-2

Cited by 32 publications

(21 citation statements)

References 10 publications

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“…Spanners are used as a key ingredient in many applications (e.g., synchronizers [21], compact rout-ing [22,26,8], broadcasting [18], and distance oracles [27,31,10,11]). …”

Section: Introductionmentioning

confidence: 99%

Near-Optimal Light Spanners

Chechik¹,

Wulff-Nilsen²

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Spanners are used as a key ingredient in many applications (e.g., synchronizers [21], compact rout-ing [22,26,8], broadcasting [18], and distance oracles [27,31,10,11]). …”

Section: Introductionmentioning

confidence: 99%

Near-Optimal Light Spanners

Chechik¹,

Wulff-Nilsen²

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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“…in areas such as metric space searching [29,30] and broadcasting in communication networks [2,14,25]. Several well-known theoretical results also use the construction of t-spanners as a building block; for example, Rao and Smith [32] made a breakthrough by showing an optimal O(n log n)-time approximation scheme for the well-known Euclidean traveling salesperson problem, using t-spanners (or banyans).…”

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confidence: 99%

Improving the Stretch Factor of a Geometric Network by Edge Augmentation

Farshi¹,

Giannopoulos²,

Gudmundsson³

2008

SIAM J. Comput.

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Abstract. Given a Euclidean graph G in R d with n vertices and m edges, we consider the problem of adding an edge to G such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a graph with positive edge weights runs in O(nm + n 2 log n) time, resulting in a trivial O(n 3 m + n 4 log n)-time algorithm for computing the optimal edge. First, we show that a simple modification yields the optimal solution in O(n 4 ) time using O(n 2 ) space. To reduce the running time we consider several approximation algorithms.Key words. computational geometry, approximation algorithms, geometric networks AMS subject classifications. 65D18, 68U05, 68Q25 DOI. 10.1137/050635675 1. Introduction. Consider a set V of n points in R d . A network on V can be modeled as an undirected graph G with vertex set V of size n and an edge set E of size m where every edge (u, v) has a positive weight w (u, v). A Euclidean network is a geometric network where the weight of the edge (u, v) is equal to the Euclidean distance |uv| between its two endpoints u and v.For two vertices u, v in a weighted graph G we use δ G (u, v) to denote a shortest path between u and v in G, and the length of the path is denoted by d G (u, v). Consider a weighted graph G = (V, E) and a graph G = (V, E ) on the same vertex set but with edge set E ⊆ E. We say that G is a t-spanner of G if for each pair of vertices (u, v). The minimum t such that G is a t-spanner for V is called the stretch factor, or dilation, of G.We say that a Euclidean network G = (V, E) is a t-spanner if G = (V, E) is a t-spanner of the complete network on V . In other words, for any two points p, q ∈ V the graph distance in G is at most t times the Euclidean distance between the two points.Complete graphs represent ideal communication networks, but they are expensive to build; sparse spanners represent low-cost alternatives. The weight of the spanner network is a measure of its sparseness; other sparseness measures include the number of edges, the maximum degree, and the number of Steiner points. Spanners for complete Euclidean graphs as well as for arbitrary weighted graphs find applications in robotics, network topology design, distributed systems, design of parallel machines, and many other areas. Recently spanners found interesting practical applications

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“…It will be interesting to relax our model to balanced subgraphs instead of balanced trees, that is, the problem of finding a minimum weight subgraph such that the distance between any two vertices u and v in the subgraph is at most a given constant times the shortest distance between the two vertices in the underlying graph (this problem is known as t-spanner problem in the literatures). See [23], [24], [25], [26] and the references therein.…”

Section: Discussionmentioning

confidence: 99%

Genetic Algorithms for Balanced Spanning Tree Problem

Moharam

Morsy

Ismail

2015

Annals of Computer Science and Information Systems

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Abstract-Given an undirected weighted connected graph G = (V, E) with vertex set V and edge set E and a designated vertex r ∈ V , we consider the problem of constructing a spanning tree in G that balances both the minimum spanning tree and the shortest paths tree rooted at r. Formally, for any two constants α, β ≥ 1, we consider the problem of computing an (α, β)-balanced spanning tree T in G, in the sense that, (i) for every vertex v ∈ V , the distance between r and v in T is at most α times the shortest distance between the two vertices in G, and (ii) the total weight of T is at most β times that of the minimum tree weight in G. It is well known that, for any α, β ≥ 1, the problem of deciding whether G contains an (α, β)-balanced spanning tree is NP-complete [15]. Consequently, given any α ≥ 1 (resp., β ≥ 1), the problem of finding an (α, β)-balanced spanning tree that minimizes β (resp., α) is NP-complete. In this paper, we present efficient genetic algorithms for these problems. Our experimental results show that the proposed algorithm returns high quality balanced spanning trees.

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Spanners and message distribution in networks

Cited by 32 publications

References 10 publications

Near-Optimal Light Spanners

Near-Optimal Light Spanners

Improving the Stretch Factor of a Geometric Network by Edge Augmentation

Genetic Algorithms for Balanced Spanning Tree Problem

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