In this paper we present the main algorithmic challenges that large Web search engines face today. These challenges are present in all the modules of a Web retrieval system, ranging from the gathering of the data to be indexed (crawling) to the selection and ordering of the answers to a query (searching and ranking). Most of the challenges are ultimately related to the quality of the answer or the efficiency in obtaining it, although some are relevant even to the existence of search engines: context based advertising.

Dubbed the ``architects of eukaryotic complexity'', RNA molecules are increasingly in the spotlight, in recognition of the important catalytic and regulatory roles they play in our cells and their promise in therapeutics. Our goal is to describe the ways in which algorithms can help shape our understanding of RNA structure and function.

In this talk we present several results and open problems having squares, the basic geometric entity, as a common thread. These results have been gathered from various papers; coauthors and precise references are given in the descriptions that follow.

We describe a very simple idea for designing approximation algorithms for connectivity problems: For a spanning tree problem, the idea is to start with the empty set of edges, and add matching paths between pairs of components in the current graph that have desirable properties in terms of the objective function of the spanning tree problem being solved. Such matching augment the solution by reducing the number of connected components to roughly half their original number, resulting in a logarithmic number of such matching iterations. A logarithmic performance ratio results for the problem by appropriately bounding the contribution of each matching to the objective function by that of an optimal solution.

In this survey, we trace the initial application of these ideas to traveling salesperson problems through a simple tree pairing observation down to more sophisticated applications for buy-at-bulk type network design problems.

The theory of error-correction has had two divergent schools of thought, going back to the works of Shannon and Hamming. In the Shannon school, error is presumed to have been effected probabilistically. In the Hamming school, the error is modeled as effected by an all-powerful adversary. The two schools lead to drastically different limits. In the Shannon model, a binary channel with error-rate close to, but less than, 50\% is useable for effective communication. In the Hamming model, a binary channel with an error-rate of more than 25\% prohibits unique recovery of the message.

In this talk, we describe the notion of list-decoding, as a bridge between the Hamming and Shannon models. This model relaxes the notion of recovery to allow for a "list of candidates". We describe results in this model, and then show how these results can be applied to get unique recovery under "computational restrictions" on the channel's ability, a model initiated by R.~Lipton in 1994.

Based on joint works with Venkatesan Guruswami (U. Washington), and with Silvio Micali (MIT), Chris Peikert (MIT) and David Wilson (MIT).

This plenary talk gives an overview of recent joint work with G. Caire and S. Shamai on the use of linear error correcting codes for lossless data compression, joint source/channel coding and interactive data exchange.

Humanity has grappled with the meaning and utility of randomness for centuries. Research in the Theory of Computation in the last thirty years has enriched this study considerably. We describe two main aspects of this research on randomness, demonstrating its power and weakness respectively.

We consider a multiprocessor operating system in which each current job is guaranteed a given proportion over time of the total processor capacity. A scheduling algorithm allocates units of processor time to appropriate jobs at each time step. We measure the goodness of such a scheduler by the maximum amount by which the cumulative processor time for any job ever falls below the ``fair'' proportion guaranteed in the long term.

In particular we focus our attention on very simple schedulers which impose minimal computational overheads on the operating system. For several such schedulers we obtain upper and lower bounds on their deviations from fairness. The scheduling quality which is achieved depends quite considerably on the relative processor proportions required by each job.

We will outline the proofs of some of the upper and lower bounds, both for the unrestricted problem and for restricted versions where constraints are imposed on the processor proportions. Many problems remain to be investigated and we will give the results of some exploratory simulations.

This is joint research with Micah Adler, Petra Berenbrink, Tom Friedetzky, Leslie Ann Goldberg and Paul Goldberg.

In this lecture, I will show how influential has been the work of Imre in the theory of automata, languages and semigroups. I will mainly focus on two celebrated problems, the restricted star-height problem (solved) and the decidability of the dot-depth hierarchy (still open). These two problems lead to surprising developments and are currently the topic of very active research.

I will present the prominent results of Imre on both topics, and demonstrate how these results have been the motor nerve of the research in this area for the last thirty years.

I will propose a general framework for the static analysis of programs based on Kleene algebra with tests (KAT). I will show how KAT can be used to statically verify compliance with safety policies specified by security automata. The method is sound and complete over relational interpretations. I will illustrate the method on an example involving the correctness of a device driver.

Phase transitions are familiar phenomena in physical systems. But they also occur in many probabilistic and combinatorial models, including random versions of some classic problems in theoretical computer science.

In this talk, I will discuss phase transitions in several systems, including the random graph -- a simple probabilistic model which undergoes a critical transition from a disordered to an ordered phase; k-satisfiability -- a canonical model in theoretical computer science which undergoes a transition from solvability to insolvability; and optimum partitioning -- a fundamental problem in combinatorial optimization, which undergoes a transition from existence to non-existence of a perfect optimizer.

Technically, phase transitions only occur in infinite systems. However, real systems and the systems we simulate are large, but finite. Hence the question of finite-size scaling: Namely, how does the transition behavior emerge from the behavior of large, finite systems? Results on the random graph, satisfiability and optimum partitioning locate the critical windows of these transitions and establish interesting features within these windows.

No knowledge of phase transitions will be assumed in this talk

The Internet and the worldwide web, unlike all other computational artifacts, were not deliberately designed by a single entity, but emerged from the complex interactions of many. As a result, they must be approached very much the same way that cells, galaxies or markets are studied in other sciences: By speculative (and falsifiable) theories trying to explain how selfish algorithmic actions could have led to what we observe. I present several instances of recent work on this theme, with several collaborators

The Probabilistic Method is a lasting legacy of the late Paul Erdos. We give two examples - both problems first formulated by Erdos in the 1960s with new results in the last few years and both with substantial open questions. Further in both examples we take a Computer Science vantagepoint, creating a probabilistic algorithm to create the object (coloring, packing respectively) and showing that with positive probability the created object has the desired properties.

Given m sets each of size n (with an arbitrary intersection pattern) we want to color the underlying vertices Red and Blue so that no set is monochromatic. Erdos showed this may always be done if m< 2(n-1), we give a recent argument of Srinivasan and Radhukrishnan that extends this to m < c 2n\sqrt{n/\ln n}. One first colors randomly and then recolors the blemishes with a clever random sequential algorithm.

In a universe of size N we have a family of sets, each of size k, such that each vertex is in D sets and any two vertices have only o(D) common sets. Asymptotics are for fixed k with N,D. We want an asymptotic packing, a subfamily of N/k disjoint sets. Erdos and Hanani conjectured such a packing exists (in an important special case of asymptotic designs) and this conjecture was shown by Rodl. We give a simple proof of the speaker that analyzes the random greedy algorithm.

In this paper we present a collection of problems which have defied solution for some time. We hope that this paper will stimulate renewed interest in these problems, leading to solutions to at least some of them.

Finite state machines have been used to model a wide variety of systems, including sequential circuits, communication protocols, and other types of reactive systems, i.e., systems that interact with their environment. In testing problems we are given a system, which we may test by providing inputs and observing the outputs produced.

The goal is to design test sequences so that we can deduce desired information about the given system under test, such as whether it implements correctly a given specification machine (conformance testing), or whether it satisfies given requirement properties (black-box checking).

In this talk we will review some of the theory and algorithms on basic testing problems for systems modeled by different types of finite state machines. Conformance testing of deterministic machines has been investigated for a long time; we will discuss various efficient methods. Testing of nondeterministic and probabilistic machines is related to games with incomplete information and to partially observable Markov decisions processes.

The verification of properties for finite state systems with a known structure (i.e., "white box" checking) is known as the model-checking problem, and has been thoroughly studied for many years, yielding a rich theory, algorithms and tools. Black-box checking, i.e., the verification of properties for systems with an unknown structure, combines elements from model checking, conformance testing and learning.