Lecture 2 : Karger ’ s Min Cut Algorithm
نویسنده
چکیده
(These notes are a slightly modified version of notes from previous offerings of the class scribed by Sanjeev.) Today’s topic is simple but gorgeous: Karger’s min cut algorithm and its extension. It is a simple randomized algorithm for finding the minimum cut in a graph: a subset of vertices S in which the set of edges leaving S, denoted E(S, S) has minimum size among all subsets. You may have seen an algorithm for this problem in your undergrad class that/ uses maximum flow. Karger’s algorithm is elementary and and a great introduction to randomized algorithms.
منابع مشابه
on Karger ’ s Min - Cut Algorithm
Traditionally, the min-cut problem was solved by solving n − 1 min-st-cut problems. In the min-st-cut problem we are given as input two vertices s and t, our aim is to find the set S where s ∈ S and t / ∈ S which minimizes the size of the cut (S, S), i.e., |δ(S)|. The size of the min-st-cut is equal to the value of the max-st-flow (equivalent by linear programming duality). The fastest algorith...
متن کاملSixth Cargese Workshop on Combinatorial Optimization Lecture 3: Sparsifiers
In this last lecture we will discuss graph sparsification: approximating a graph by weighted subgraphs of itself. Sparsifications techniques have been used to design fast algorithms for combinatorial or linear algebraic problems, as a rounding technique in approximation algorithms, and have motivated startling results in pure mathematics. 1 Spectral Sparsifiers Let G = (V,E) be a graph with V =...
متن کامل.1 First Try 1.2 Second Try
Suppose we are given a graph G = (V,E). We would like to solve some cut problem (i.e. min-cut, s-t min cut, sparsest cut) and so on. The running time of algorithms for these problems typically depends on the number of edges in the graph, which might be as high as O(n). Is there any way to approximate our graph with a sparse graph G′ in which all cuts are approximately of the same size? We will ...
متن کاملMin Cut , Fast Cut , Polynomial Identities
Throughout this section, G = (V,E) is a multi-graph. A cut of G is a bipartition (S, S̄) of the vertex set of G. The capacity of a cut is the number of edges having one endpoint on both sides of the cut. A min-cut is a cut of minimum capacity. A minimum cut can be computed with the help of maxflow computations. For some vertex s and every other vertex t, one computes the minimum cut separating s...
متن کاملGlobal Min-cuts in RNC, and Other Ramifications of a Simple Min-Cut Algorithm
This paper presents a new algorithm for nding global min-cuts in weighted, undirected graphs. One of the strengths of the algorithm is its extreme simplicity. This randomized algorithm can be implemented as a strongly polynomial sequential algorithm with running time ~ O(mn 2), even if space is restricted to O(n), or can be parallelized as an RNC algorithm which runs in time O(log 2 n) on a CRC...
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 2016