Approximating the Minimum Bisection Size
نویسندگان
چکیده
A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NP-hard. We present an algorithm that nds a bisection that is within O(p n log n) of optimal. No sublinear approximation ratio for bisection was previously known.
منابع مشابه
Strengthened Hardness for Approximating Minimum Unique Game and Small Set Expansion
In this paper, the author puts forward a variation of Feige’s Hypothesis, which claims that it is hard on average refuting Unbalanced Max 3-XOR against biased assignments on a natural distribution. Under this hypothesis, the author strengthens the previous known hardness for approximating Minimum Unique Game, 5/4 − ǫ, by proving that Min 2-Lin-2 is hard to within 3/2 − ǫ and strengthens the pre...
متن کاملCoping with Np-hardness: Approximating Minimum Bisection and Heuristics for Maximum Clique 2 Approximating Minimum Bisection 13 1.2 Approximation Algorithms
Many important optimization problems are known to be NP-hard. That is, unless P = NP, there is no polynomial time algorithm that optimally solves these problems on every input instance. We study algorithmic ways for \coping" with NP-hard optimization problems. One possible approach for coping with the NP-hardness is to relax the requirement for exact solution, and devise approximation algorithm...
متن کاملA polylogarithmic approximation of the minimum bisection
A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets. Finding the bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of O(log2 n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) we ...
متن کاملOn the Parameterized Complexity of Computing Graph Bisections
The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that Bisection is FPT w.r.t. the minimum c...
متن کاملThe Minimum Bisection in the Planted Bisection Model
In the planted bisection model a random graph G(n, p+, p−) with n vertices is created by partitioning the vertices randomly into two classes of equal size (up to ±1). Any two vertices that belong to the same class are linked by an edge with probability p+ and any two that belong to different classes with probability p− < p+ independently. The planted bisection model has been used extensively to...
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