The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this “deterministic random walk” covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several impo...

We use mobile guards on the vertices of a graph to defend it against an infinite sequence of attacks on its edges. A guard on an incident vertex moves across the attacked edge to defend it; other guards may also move to neighboring vertices. We prove upper and lower bounds on the minimum number of guards needed for this eternal vertex cover problem and characterize the graphs for which the uppe...

We modify W. Vickrey's (1961, J. Finance 16, 8 37) mechanism for call markets by introducing the participation stage and study the efficiency properties of the modified mechanism. We provide sufficient conditions under which the modified Vickrey double auction achieves full efficiency. In addition, we prove that the modified Vickrey double auction achieves asymptotic efficiency even when full e...

Mechanical drift is a long-standing problem in optical microscopy that occurs in all three dimensions. This drift increasingly limits the resolution of advanced surface-coupled, single-molecule experiments. We overcame this drift and achieved atomic-scale stabilization (0.1 nm) of an optical microscope in 3D. This was accomplished by measuring the position of a fiducial mark coupled to the micr...

The calculation of an exact minimal cover of a Boolean function is an NP -complete problem. In this paper we introduce the definition of this problem and its basic solution. By using a slightly modified algorithm, we get a speed-up factor of more than 10. The main contributions of this paper are the description of an alternative approach mentioned in [15], and a remarkable improvement of this a...

Using satellite radar interferometry observations of Greenland, we detected widespread glacier acceleration below 66 degrees north between 1996 and 2000, which rapidly expanded to 70 degrees north in 2005. Accelerated ice discharge in the west and particularly in the east doubled the ice sheet mass deficit in the last decade from 90 to 220 cubic kilometers per year. As more glaciers accelerate ...

We take a new look at the multicut problem in trees through the eyes of the vertex cover problem. This connection, together with other techniques that we develop, allows us to significantly improve the O(k) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O∗(ρk),...

A set P of edge-disjoint paths in a graph G is called an edge-covering of G if every edge of G is contained in a path of P. The path edge-covering number of G is then defined as the smallest number p(G) of paths in such an edge-covering of G. This parameter appeared in the study of certain models of information retrieval structures (see, e. g., [6]). If we are considering a tree T , then it is ...

We consider a natural generalization of the classical minimum hitting set problem, the minimum hitting set of bundles problem (mhsb) which is defined as follows. We are given a set E = {e1, e2, . . . , en} of n elements. Each element ei (i = 1, . . . , n) has a non negative cost ci. A bundle b is a subset of E . We are also given a collection S = {S1, S2, . . . , Sm} of m sets of bundles. More ...

The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order O(c), but with the co...