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In this paper we consider the problem of (<i>k</i>, <i>υ</i>)-balanced graph partitioning - dividing the vertices of a graph into <i>k</i> almost equal size components (each of size less than <i>υ</i> • <i>n</i><over><i>k</i>) so that the capacity of edges between different components is minimized. This problem is a natural… (More)

- Harald Räcke
- STOC
- 2008

Hierarchical graph decompositions play an important role in the design of approximation and online algorithms for graph problems. This is mainly due to the fact that the results concerning the approximation of metric spaces by tree metrics (e.g. [10,11,14,16]) depend on hierarchical graph decompositions. In this line of work a probability distribution over… (More)

We introduce the online scheduling problem for sorting buffers. A service station and a sorting buffer are given. An input sequence of items which are only characterized by a specific attribute has to be processed by the service station which benefits from consecutive items with the same attribute value. The sorting buffer which is a random access buffer… (More)

- Harald Räcke
- FOCS
- 2002

A principle task in parallel and distributed systems is to reduce the communication load in the interconnection network, as this is usually the major bottleneck for the performance of distributed applications. In this paper we introduce a framework for solving on-line problems that aim to minimize the congestion (i.e. the maximum load of a network link) in… (More)

A recent seminal result of Racke is that for any network there is an oblivious routing algorithm with a polylog competitive ratio with respect to congestion. Unfortunately, Racke's construction is not polynomial time. We give a polynomial time construction that guarantee's Racke's bounds, and more generally gives the true optimal ratio for any network.

We study rerouting policies in a dynamic round-based variant of a well known game theoretic traffic model due to Wardrop. Previous analyses (mostly in the context of selfish routing) based on Wardrop's model focus mostly on the static analysis of equilibria. In this paper, we ask the question whether the population of agents responsible for routing the… (More)

We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node… (More)

In this article, we study metrics of <i>negative type</i>, which are metrics (<i>V</i>, d) such that &sqrt;d is an Euclidean metric; these metrics are thus also known as ℓ<sub>2</sub>-squared metrics. We show how to embed <i>n</i>-point negative-type metrics into Euclidean space ℓ<sub>2</sub> with distortion <i>D</i> =… (More)

Consider the following network design problem: given a network <i>G = (V, E)</i>, source-sink pairs {<i>s</i><inf><i>i</i></inf>, <i>t</i><inf><i>i</i></inf>} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge <i>e</i> carries a total of <i>f</i><inf><i>e</i></inf> flow (from all the terminal pairs), the… (More)

We give almost tight bounds for the online reordering buffer management problem on the uniform metric. Specifically, we present the first non-trivial lower bounds for this problem by showing that deterministic online algorithms have a competitive ratio of at least Ω(√{log k/log log k}) and randomized online algorithms have a competitive ratio of… (More)