The Bisection of Random Graphs: Rigorous Bounds Using the Analysis of Algorithms
نویسنده
چکیده
Given a random graph G = G n;1=2 , we give almost sure bounds for the value of the minimum bisection of G. The lower bound is obtained by applying the rst moment method, while the upper bound is given by the analysis of a simple algorithm. Moreover, these results enable us to derive upper bounds for the maximum bisection and the maxcut of G.
منابع مشابه
Bounds on the max and min bisection of random cubic and random 4-regular graphs
In this paper, we present a randomized algorithm to compute the bisection width of cubic and 4-regular graphs. The analysis of the proposed algorithms on random graphs provides asymptotic upper bounds for the bisection width of random cubic and random 4-regular graphs with n vertices, giving upper bounds of 0:174039n for random cubic, and of 0:333333n for random 4-regular. We also obtain asympt...
متن کاملBounds on the bisection width for random d -regular graphs
In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d-regular graphs, for any value of d. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We provide bounds for 5 ≤ d ≤ 12. We also give empirical values of the size of the bisection f...
متن کاملA conjecture on the maximum cut and bisection width in random regular graphs
The asymptotic properties of random regular graphs are objects of extensive study in mathematics and physics. In this paper we argue, using the theory of spin glasses in physics, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no ...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملConjecture on the maximum cut and bisection width in random regular graphs
Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no known general relation between...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000