Dr. Heinz Karger †

MEMORIAL ISSUE DEDICATED TO THE 100TH BIRTHDAY OF LATE UNIV. – PROF. DR. KARL HEINZ RECHINGER

Karl Heinz Rechinger was born on October 16, 1906 at Vienna (Austria). He was the only son of Dr. Karl Rechinger and Rosa Elisabeth Rechinger née Favarger. His father was also a plant taxonomist. The principal focus of K.H. Rechinger was flora writing. He was the author of Flora Aegaea and founder and editor of "Flora Iranica". In 1929, Rechinger started to work as an unpaid volunteer in the De...

Heinz Nixdorf Institute Heinz Nixdorf

Graph Coloring ( 1994 , 1998 ; Karger , Motwani , Sudan )

An independent set in an undirected graph G = (V,E) is a set of vertices that induce a subgraph which does not contain any edges. The size of the maximum independent set in G is denoted by α(G). For an integer k, a k-coloring of G is a function σ : V → [1 . . . k] which assigns colors to the vertices of G. A valid k-coloring of G is a coloring in which each color class is an independent set. Th...

Lecture 2 : Karger ’ s Min Cut Algorithm

(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 ...

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...