On certain connectivity properties of the Internet topology

Mihail, Milena; Papadimitriou, C.; Saberi, Amin

doi:10.1109/sfcs.2003.1238178

Cited by 38 publications

(29 citation statements)

References 30 publications

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“…Mihail, Papadimitriou and Saberi [12] proved that the conductance Φ(G(m, n)) of a simple random walk on G(m, n) is bounded below by an absolute constant Φ > 0 (whp). We will form a graph Γ by contracting some set of vertices of G(m, n) to single vertex γ.…”

Section: Mixing Time Of Walks On G(m N)mentioning

confidence: 99%

Random Walks with Look-Ahead in Scale-Free Random Graphs

Cooper¹,

Frieze²

2010

SIAM J. Discrete Math.

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Section: Mixing Time Of Walks On G(m N)mentioning

confidence: 99%

Random Walks with Look-Ahead in Scale-Free Random Graphs

Cooper¹,

Frieze²

2010

SIAM J. Discrete Math.

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“…In [AT02,AT07] it is shown that any truthful mechanism has bad worst-case s-t path overpayment. Additional investigations of shortest paths in a worst-case setting appear in [MPS03,ESS04,CR04,Elk05].…”

Section: Introductionmentioning

confidence: 99%

“…Another alternative, and the one we adopt here, is to compare the VCG cost with the minimum cost in an average-case setting. This was done for shortest paths in certain graphs in [MPS03,CR04,KN05,FGS06]. We consider the expected VCG overpayment in three settings, in each of which the expected minimum cost is a classical result in the analysis of random structures.…”

Section: Introductionmentioning

confidence: 99%

Average-Case Analyses of Vickrey Costs

Chebolu

Frieze

Melsted

et al. 2009

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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Abstract. We explore the average-case "Vickrey" cost of structures in a random setting: the Vickrey cost of a shortest path in a complete graph or digraph with random edge weights; the Vickrey cost of a minimum spanning tree (MST) in a complete graph with random edge weights; and the Vickrey cost of a perfect matching in a complete bipartite graph with random edge weights. In each case, in the large-size limit, the Vickrey cost is precisely 2 times the (non-Vickrey) minimum cost, but this is the result of case-specific calculations, with no general reason found for it to be true.Separately, we consider the problem of sparsifying a complete graph with random edge weights so that all-pairs shortest paths are preserved approximately. The problem of sparsifying a given graph so that for every pair of vertices, the length of the shortest path in the sparsified graph is within some multiplicative factor and/or additive constant of the original distance has received substantial study in theoretical computer science. For the complete graph Kn with additive edge weights, we show that whp Θ(n ln n) edges are necessary and sufficient for a spanning subgraph to give good all-pairs shortest paths approximations.

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“…See [AT02] for a detailed study of the worst-case behavior of this overpayment. Additional investigation of shortest paths in this setting appear in [MPS03,ESS04,CR04,Elk05]. It is possible that the worst-case bounds on the cost of the VCG mechanism are overly pessimistic.…”

Section: Introductionmentioning

confidence: 99%

“…To investigate this, we compare the cost of the VCG mechanism with the shortest-path cost in the average-case setting (for the width-2 strip with random edge costs). Other average-case studies for completely different graphs appear in [MPS03,CR04], and real-world measurements appear in [FPSS02]. Generalizations: We rely on no special properties of the uniform distribution; the methods we use to analyze this edge-length distribution could equally well be applied to any well-behaved, bounded distribution.…”

Section: Introductionmentioning

confidence: 99%

First-Passage Percolation on a Width-2 Strip and the Path Cost in a VCG Auction

Flaxman

Gamarnik²,

Sorkin

2006

Lecture Notes in Computer Science

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ABSTRACT. We study the time constant for first-passage percolation, and the Vickery-Clarke-Groves (VCG) payment for the shortest path, on a width-2 strip with random edge costs. These statistics attempt to describe two seemingly unrelated phenomena, arising in physics and economics respectively: the first-passage percolation time predicts how long it takes for a fluid to spread through a random medium, while the VCG payment for the shortest path is the cost maximizing social welfare among selfish agents. However, our analyses of the two are quite similar, and require solving (slightly different) recursive distributional equations. Using Harris chains, we can characterize distributions, not just expectations.

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On certain connectivity properties of the Internet topology

Cited by 38 publications

References 30 publications

Random Walks with Look-Ahead in Scale-Free Random Graphs

Random Walks with Look-Ahead in Scale-Free Random Graphs

Average-Case Analyses of Vickrey Costs

First-Passage Percolation on a Width-2 Strip and the Path Cost in a VCG Auction

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