Marek Chrobak

Fast broadcasting and gossiping in radio networks

We establish an O(nlog2n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of Ω(n log n). The fastest previously known algorithm for this problem works in time O(n3/2). Using our broadcasting algorithm, we develop an O(n3/2log2n) algorithm for gossiping in the same network model.

Analysis of Bacterial Community Composition by Oligonucleotide Fingerprinting of rRNA Genes

ABSTRACT One of the first steps in characterizing an ecosystem is to describe the organisms inhabiting it. For microbial studies, experimental limitations have hindered the ability to depict diverse communities. Here we describe oligonucleotide fingerprinting of rRNA genes (OFRG), a method that permits identification of arrayed rRNA genes (rDNA) through a series of hybridization experiments using small DNA probes. To demonstrate this strategy, we examined the bacteria inhabiting two different soils. Analysis of 1,536 rDNA clones revealed 766 clusters grouped into five major taxa: Bacillus, Actinobacteria, Proteobacteria, and two undefined assemblages. Soil-specific taxa were identified and then independently confirmed through cluster-specific PCR of the original soil DNA. Near-species-level resolution was obtained by this analysis as clones with average sequence identities of 97% were grouped in the same cluster. A comparison of these OFRG results with the results obtained in a denaturing gradient gel electrophoresis analysis of the same two soils demonstrated the significance of this methodological advance. OFRG provides a cost-effective means to extensively analyze microbial communities and should have applications in medicine, biotechnology, and ecosystem studies.

A linear-time algorithm for drawing a planar graph on a grid

Abstract We present a linear-time algorithm that, given an n -vertex planar graph G , finds an embedding of G into a (2 n − 4) × ( n − 2) grid such that the edges of G are straight-line segments.

Reconstructing hv-convex polyominoes from orthogonal projections

Abstract We address the problem of reconstructing a discrete 2D object, represented by a set of grid cells, from its orthogonal projections. We focus on objects called hv-convex polyominoes, which are connected objects with the property that the cells in each row and column are consecutive. The main result of this paper is a simple, O(mn min(m2,n2))-time algorithm for reconstructing hv-convex polyominoes.

An optimal on-line algorithm for K-servers on trees

The k-server problem is investigated when the metric space is a tree. For this case an on-line k-competitive algorithm for k-servers is presented. The competitiveness ratio k is optimal. The algorithm is memoryless, in the sense that it does not use any information from the past.

Dynamic Thermal Management through Task Scheduling

The evolution of microprocessors has been hindered by their increasing power consumption and the heat generation speed on-die. High temperature impairs the processors reliability and reduces its lifetime. While hardware level dynamic thermal management (DTM) techniques, such as voltage and frequency scaling, can effectively lower the chip temperature when it surpasses the thermal threshold, they inevitably come at the cost of performance degradation. We propose an OS level technique that performs thermal- aware job scheduling to reduce the number of thermal trespasses. Our scheduler reduces the amount of hardware DTMs and achieves higher performance while keeping the temperature low. Our methods leverage the natural discrepancies in thermal behavior among different workloads, and schedule them to keep the chip temperature below a given budget. We develop a heuristic algorithm based on the observation that there is a difference in the resulting temperature when a hot and a cool job are executed in a different order. To evaluate our scheduling algorithms, we developed a lightweight runtime temperature monitor to enable informed scheduling decisions. We have implemented our scheduling algorithm and the entire temperature monitoring framework in the Linux kernel. Our proposed scheduler can remove 10.5-73.6% of the hardware DTMs in various combinations of workloads in a medium thermal environment. As a result, the CPU throughput was improved by up to 7.6% (4.1% on average) even under a severe thermal environment.

Competitive analysis of randomized paging algorithms

The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p, a miss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made on-line, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized on-line paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the competitive ratio of the marking algorithm is exactly 2Hk−1. Previously, it was known to be between Hk and 2Hk. Then we provide a new, Hk-competitive algorithm for paging. Our algorithm, as well as its analysis, is simpler than the known algorithm by McGeoch and Sleator. Another advantage of our algorithm is that it can be implemented with complexity bounds independent of the number of past requests: O(k2logk) memory and O(k2) time per request.

Planar orientations with low out-degree and compaction of adjacency matrices

Abstract We consider the problem of orienting the edges of a planar graph in such a way that the out-degree of each vertex is minimized. If, for each vertex v , the out-degree is at most d , then we say that such an orientation is d -bounded. We prove the following results: • Each planar graph has a 5-bounded acyclic orientation, which can be constructed in linear time. • Each planar graph has a 3-bounded orientation, which can be constructed in linear time. • A 6-bounded acyclic orientation, and a 3-bounded orientation, of each planar graph can each be constructed in parallel time O(log n log ∗ n ) on an EREW PRAM, using O( n /log n log ∗ n ) processors. As an application of these results, we present a data structure such that each entry in the adjacency matrix of a planar graph can be looked up in constant time. The data structure uses linear storage, and can be constructed in linear time.

LRU is better than FIFO

Abstract. In the paging problem we have to manage a two-level memory system, in which the first level has short access time but can hold only up to k pages, while the second level is very large but slow. We use competitive analysis to study the relative performance of the two best known algorithms for paging, LRU and FIFO. Sleator and Tarjan proved that the competitive ratio of LRU and FIFO is k . In practice, however, LRU is known to perform much better than FIFO. It is believed that the superiority of LRU can be attributed to locality of reference exhibited in request sequences. In order to study this phenomenon, Borodin et al. [2] refined the competitive approach by introducing the concept of access graphs. They conjectured that the competitive ratio of LRU on each access graph is less than or equal to the competitive ratio of FIFO. We prove this conjecture in this paper.

Reducing large internet topologies for faster simulations

In this paper, we develop methods to “sample” a small realistic graph from a large real network. Despite recent activity, the modeling and generation of realistic graphs is still not a resolved issue. All previous work has attempted to grow a graph from scratch. We address the complementary problem of shrinking a graph. In more detail, this work has three parts. First, we propose a number of reduction methods that can be categorized into three classes: (a) deletion methods, (b) contraction methods, and (c) exploration methods. We prove that some of them maintain key properties of the initial graph. We implement our methods and show that we can effectively reduce the nodes of a graph by as much as 70% while maintaining its important properties. In addition, we show that our reduced graphs compare favourably against construction-based generators. Apart from its use in simulations, the problem of graph sampling is of independent interest.