In 1998, Paturi, Pudlák, Saks, and Zane presented PPSZ, an elegant randomized algorithm for k-SAT. Fourteen years on, this algorithm is still the fastest known worst-case algorithm. They proved that its expected running time on k-CNF formulas with n variables is at most 2(1− k, where k ∈ Ω(1/k). So far, no exponential lower bounds at all have been known. In this paper, we construct hard instanc...

This paper examines the problem of distributed resource allocation in different models of computation and communication in distributed systems, and presents a number of time optimal (randomized and deterministic) allocation algorithms. We consider the dining drinking philosophers problem as presented in [B. Awerbuch and M. Saks, in ``FOCS,'' pp. 65 74. IEEE, New York, 1990]. In the algorithm pr...

3. N. Dunford and B. J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 323-392. 4. O. Nikodym, Sur une generalisation des integrates de M. Radon, Fund. Math, vol. 15 (1930) pp. 137-179. 5. R. S. Phillips, Integration in convex linear topological space, Trans. Amer. Math. Soc. vol. 48 (1940) pp. 516-540. 6. C. E. Rickart, Integration in a convex linear...

Motivated by a dynamic location problem for graphs, Chung, Graham and Saks introduced a graph parameter called windex. Graphs of windex 2 turned out to be, in graph-theoretic language, retracts of hypercubes. These graphs are also known as median graphs and can be characterized as partial binary Hamming graphs satisfying a convexity condition. In this paper an O(n 3 2 logn) algorithm is present...

The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary (Ambainis, 2003), strong weighted adversary (Zhang, 2005), and the Kolmogorov complexity adversary (Laplante and Magniez, 2004). We also present a few new equi...

In a classical 1986 paper by Erdös, Saks and Sós every graph of radius r has an induced path of order at least 2r − 1. This result implies that the independence number of such graphs is at least r . In this paper, we use a result of S. Fajtlowicz about radius-critical graphs to characterize graphs where the independence number is equal to the radius, for all possible values of the radius except...