Yair Bartal

On approximating arbitrary metrices by tree metrics

We design a generation algorithm for a problem which a&es in computational chemistry: the random generation of models of amorphous strutures. Such structures can be modeled as graphs which see embedded in d-space. The algorithm uses the well known approach of simulating a rapidly-mixing Markov chain. Gur analysis of the Mixing rate is based on Dobrushin uniqueness. The structure of the problem forces us to extend the basic method and find an alternative to Dobrushin’s condition which is more appropriate for our problem. This extension appears to be of more general interest.

Firmato : A novel firewall management toolkit

In recent years packet-filtering firewalls have seen some impressive technological advances (e.g., stateful inspection, transparency, performance, etc.) and wide-spread deployment. In contrast, firewall and security <i>management</i> technology is lacking. In this paper we present <i>Firmato</i>, a firewall management toolkit, with the following distinguishing properties and components: (1) an entity-relationship model containing, in a unified form, global knowledge of the security policy and of the network topology; (2) a model definition language, which we use as an interface to define an instance of the entity-relationship model; (3) a model compiler, translating the global knowledge of the model into firewall-specific configuration files; and (4) a graphical firewall rule illustrator. We implemented a prototype of our toolkit to work with several commercially available firewall products. This prototype was used to control an operational firewall for several months. We believe that our approach is an important step toward streamlining the process of configuring and managing firewalls, especially in complex, multi-firewall installations.

New algorithms for an ancient scheduling problem

We consider the on-line version of the original <italic>m</italic>-machine scheduling problem: given <italic>m</italic> machines and <italic>n</italic> positive real jobs, schedule the <italic>n</italic> jobs on the <italic>m</italic> machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as job <italic>j</italic> arrrives, it must be assigned immediately to one of the <italic>m</italic> machines. We present two main results. The first is a (2–ε)-competitive deterministic algorithm for all <italic>m</italic>. The competitive ratio of all previous algorithms approaches 2 as <italic>m</italic>→<inline-equation> <f> ∞</f> </inline-equation>. Indeed, the problem of improving the competitive ratio for large <italic>m</italic> had been open since 1966, when the first algorithm for this problem appeared. The second result is an optimal randomized algorithm for the case <italic>m</italic> = 2. To the best of our knowledge, our 4/3-competitive algorithm is the first specifically randomized algorithm for the original, <italic>m</italic>-machine, on-line scheduling problem.

Firmato: a novel firewall management toolkit

In recent years, packet filtering firewalls have seen some impressive technological advances (e.g., stateful inspection, transparency, performance, etc.) and widespread deployment. In contrast, firewall and security management technology is lacking. We present Firmato, a firewall management toolkit, with the following distinguishing properties and components: (1) an entity relationship model containing, in a unified form, global knowledge of the security policy and of the network topology; (2) a model definition language, which we use as an interface to define an instance of the entity relationship model; (3) a model compiler translating the global knowledge of the model into firewall-specific configuration files; and (4) a graphical firewall rule illustrator. We demonstrate Firmatos capabilities on a realistic example, thus showing that firewall management can be done successfully at an appropriate level of abstraction. We implemented our toolkit to work with a commercially available firewall product. We believe that our approach is an important step towards streamlining the process of configuring and managing firewalls, especially in complex, multi firewall installations.

Incentive compatible multi unit combinatorial auctions

This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.

Multiprocessor Scheduling with Rejection

We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, with each job characterized by a processing time and a penalty. In the on-line version the jobs become available one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a 1 + 2:618 competitive algorithm for the on-line version of the problem, where is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For xed m we give improved bounds; in particular, for m = 2 we give a 1:618 competitive algorithm, which is best possible. For the o-line problem we present a fully polynomial approximation scheme for xed m and a polynomial approximation scheme for arbitrarym. Moreover, we present an approximation algorithm which runs in time O(n logn) for arbitrary m and guarantees a 2i 1 m approximation ratio.

Competitive algorithms for distributed data management

We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem, where copies of a file may be be stored in the local storage of some subsets of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for on-line data tracking (a generalization of mobile user tracking) to transform our competitive data management algorithms into distributed algorithms themselves.

Global optimization using local information with applications to flow control

Flow control in high speed networks requires distributed routers to make fast decisions based only on local information in allocating bandwidth to connections. While most previous work on this problem focuses on achieving local objective functions, in many cases it may be necessary to achieve global objectives such as maximizing the total flow. This problem illustrates one of the basic aspects of distributed computing: achieving global objectives using local information. Papadimitriou and Yannakakis (1993) initiated the study of such problems in a framework of solving positive linear programs by distributed agents. We take their model further, by allowing the distributed agents to acquire more information over time. We therefore turn attention to the tradeoff between the running time and the quality of the solution to the linear program. We give a distributed algorithm that obtains a (1+/spl epsiv/) approximation to the global optimum solution and runs in a polylogarithmic number of distributed rounds. While comparable in running time, our results exhibit a significant improvement on the logarithmic ratio previously obtained by Awerbuch and Azar (1994). Our algorithm, which draws from techniques developed by Luby and Nisan (1993) is considerably simpler than previous approximation algorithms for positive linear programs, and thus may have practical value in both centralized and distributed settings.

Approximating min-sum k -clustering in metric spaces

The min-sum k-clustering problem in a metric space is to find a partition of the space into k clusters as to minimize the total sum of distances between pairs of points assigned to the same cluster. We give the first polynomial time non-trivial approximation algorithm for this problem. The algorithm provides an

A polylog( n )-competitive algorithm for metrical task systems

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