Minimum coloring random and semi-random graphs in polynomial expected time

2002 ◽  
Author(s):  
C.R. Subramanian
Keyword(s):  
Random Graphs ◽  
Expected Time ◽  
Minimum Coloring

scholarly journals Speeding up non-Markovian first-passage percolation with a few extra edges

2018 ◽  
Vol 50 (3) ◽  
pp. 858-886 ◽  
Author(s):  
Alexey Medvedev ◽  
Gábor Pete
Keyword(s):  
Random Graphs ◽  
Spanning Trees ◽  
Real Life ◽  
First Passage Percolation ◽  
Power Law Distribution ◽  
First Passage ◽  
Critical Window ◽  
Expected Time ◽  
Si Model ◽  
Passage Times

Abstract One model of real-life spreading processes is that of first-passage percolation (also called the SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with independent and identically distributed heavy-tailed passage times on edges. On the other hand, random graphs are often locally tree-like, and spreading on trees with leaves might be very slow due to bottleneck edges with huge passage times. Here we consider the SI model with passage times following a power-law distribution ℙ(ξ>t)∼t-α with infinite mean. For any finite connected graph G with a root s, we find the largest number of vertices κ(G,s) that are infected in finite expected time, and prove that for every k≤κ(G,s), the expected time to infect k vertices is at most O(k1/α). Then we show that adding a single edge from s to a random vertex in a random tree 𝒯 typically increases κ(𝒯,s) from a bounded variable to a fraction of the size of 𝒯, thus severely accelerating the process. We examine this acceleration effect on some natural models of random graphs: critical Galton--Watson trees conditioned to be large, uniform spanning trees of the complete graph, and on the largest cluster of near-critical Erdős‒Rényi graphs. In particular, at the upper end of the critical window, the process is already much faster than exactly at criticality.

Coloring random graphs in polynomial expected time

1993 ◽  
pp. 31-37 ◽  
Author(s):  
Martin Furer ◽  
C. R. Subramanian ◽  
C. E. Veni Madhavan
Keyword(s):  
Random Graphs ◽  
Expected Time

A PROCESSOR EFFICIENT CONNECTIVITY ALGORITHM ON RANDOM GRAPHS

1994 ◽  
Vol 04 (01n02) ◽  
pp. 29-36
Author(s):  
S.B. YANG ◽  
S.K. DHALL ◽  
S. LAKSHMIVARAHAN
Keyword(s):  
Parallel Algorithm ◽  
Random Graphs ◽  
Connected Components ◽  
Input Graph ◽  
Random Input ◽  
Expected Time ◽  
Erew Pram ◽  
Pram Model

In this paper we present a randomized parallel algorithm for finding the connected components of a random input graph with n vertices in which the edges are chosen with probability p such that [Formula: see text]. The algorithm has O(log2 n) expected time using only O(n) processors on the EREW PRAM model. The probability that the output of our algorithm is correct is at least 1–0.6k, where k is a constant.

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs
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