Artur Czumaj

Tight bounds for worst-case equilibria

The coordination ratio is a game theoretic measure that aims to reflect the price of selfish routing in a network. We show the worst-case coordination ratio on m parallel links (of possibly different speeds) isΘ(log m/log log log m)Our bound is asymptotically tight and it entirely resolves an question posed recently by Koutsoupias and Papadimitriou [3].

Speeding up two string-matching algorithms

We show how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm). The RF algorithm is based on factor graphs for the reverse of the pattern. The main feature of both algorithms is that they scan the text right-to-left from the supposed right position of the pattern. The BM algorithm goes as far as the scanned segment (factor) is a suffix of the pattern. The RF algorithm scans while the segment is a factor of the pattern. Both algorithms make a shift of the pattern, forget the history, and start again. The RF algorithm usually makes bigger shifts than BM, but is quadratic in the worst case. We show that it is enough to remember the last matched segment (represented by two pointers to the text) to speed up the RF algorithm considerably (to make a linear number of inspections of text symbols, with small coefficient), and to speed up the BM algorithm (to make at most 2 ·n comparisons). Only a constant additional memory is needed for the search phase. We give alternative versions of an accelerated RF algorithm: the first one is based on combinatorial properties of primitive words, and the other two use the power of suffix trees extensively. The paper demonstrates the techniques to transform algorithms, and also shows interesting new applications of data structures representing all subwords of the pattern in compact form.

Selfish traffic allocation for server farms

We investigate the price of selfish routing in non-cooperative networks in terms of the coordination and bicriteria ratios in the recently introduced game theoretic network model of Koutsoupias and Papadimitriou. We present the first thorough study of this model for general, monotone families of cost functions and for cost functionsm from Queueing Theory. Our main results can be summarized as follows.We give a precise characterization of cost functions having a bounded/unbounded coordination ratio. For example, cost functions that describe the expected delay in queueing systems have an unbounded coordination ratio.We show that an unbounded coordination ratio implies additionally an extremely high performance degradation under bicriteria measures. We demonstrate that the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size.We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small, in fact negligible, amount of integrality can lead to a dramatic performance degradation.We unify recent results on selfish routing under different objectives by showing that an unbounded coordination ratio under the min-max objective implies an unbounded coordination ratio under the average-cost (or total-latency) objective and vice versa..Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of TCP connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload.From the result presented in this paper we conclude that queuing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates.

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

Fast practical multi-pattern matching

d \ge 2

Testing Expansion in Bounded-Degree Graphs

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

Testing Hereditary Properties of Nonexpanding Bounded-Degree Graphs

m \approx n

Randomized allocation processes

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

Facility location in sublinear time

m \gg n

Perfectly Balanced Allocation

rather than