Angelika Steger

Balls into Bins - A Simple and Tight Analysis

Suppose we sequentially throw m balls into n bins. It is a natural question to ask for the maximum number of balls in any bin. In this paper we shall derive sharp upper and lower bounds which are reached with high probability. We prove bounds for all values of m(n) ≥ n=polylog(n) by using the simple and well-known method of the first and second moment.

Generating Random Regular Graphs Quickly

We present a practical algorithm for generating random regular graphs. For all d growing as a small power of n, the d-regular graphs on n vertices are generated approximately uniformly at random, in the sense that all d-regular graphs on n vertices have in the limit the same probability as n → ∞. The expected runtime for these ds is O(nd2).

Random planar graphs

We study various properties of the random planar graph Rn, drawn uniformly at random from the class Pn of all simple planar graphs on n labelled vertices. In particular, we show that the probability that Rn is connected is bounded away from 0 and from 1. We also show for example that each positive integer k, with high probability Rn has linearly many vertices of a given degree, in each embedding Rn has linearly many faces of a given size, and Rn has exponentially many automorphisms.

A New Approximation Algorithm for the Steiner Tree Problem with Performance Ratio 5/3

In this paper we present an RNC approximation algorithm for the Steiner tree problem in graphs with performance ratio 5/3 and RNC approximation algorithms for the Steiner tree problem in networks with performance ratio 5/3+? for all ?0. This is achieved by considering a related problem, the minimum spanning tree problem in weighted 3-uniform hypergraphs. For that problem we give a fully polynomial randomized approximation scheme. Our approach also gives rise to conceptually much easier and faster (though randomized) sequential approximation algorithms for the Steiner tree problem than the currently best known algorithms from Karpinski and Zelikovsky which almost match their approximation factor.

Balanced Allocations: The Heavily Loaded Case

We investigate balls-into-bins processes allocating m balls into n bins based on the multiple-choice paradigm. In the classical single-choice variant each ball is placed into a bin selected uniformly at random. In a multiple-choice process each ball can be placed into one out of

Excluding induced subgraphs: quadrilaterals

d \ge 2

RNC-Approximation Algorithms for the Steiner Problem

randomly selected bins. It is known that in many scenarios having more than one choice for each ball can improve the load balance significantly. Formal analyses of this phenomenon prior to this work considered mostly the lightly loaded case, that is, when

Optimal Algorithms for k -Search with Application in Option Pricing

m \approx n

An Extremal Problem For Random Graphs And The Number Of Graphs With Large Even-Girth

. In this paper we present the first tight analysis in the heavily loaded case, that is, when

Almost all Berge Graphs are Perfect

m \gg n