We compute the regression depth of a k-flat in a set of n points in R^d, in time Ο(n^d-2 + n log n) for 1 ⪇ k ⪇ d - 2. This contrasts with a bound of Ο(n^d-1 + n log n) when k = 0 or k = d - 1.

We propose a discrete variant of the Bak-Sneppen model for self-organized criticality. In this process, a configuration is an n-bit word, and at each step one chooses a random bit of minimum value (usually a zero) and replaces it and its two neighbors ...

Many massive graphs (such as the WWW graph and Call graphs) share certain universal characteristics which can be described by so-called the “power law”. Here we determine the diameter of random power law graphs up to a constant factor for almost all ...

We explore the natural question of whether all NP-complete problems have a common restriction under which they are polynomially solvable. More precisely, we study what languages are universally easy in that their intersection with any NP-complete ...

We analyze the behavior of hill-climbing algorithms for the minimum bisection problem on instances drawn from the “planted bisection” random graph model, G_n,p,q, previously studied in [3, 4, 10, 11, 14, 9, 7]. This is one of the few problem ...

In the bus network problem, the goal is to generate a plan for getting from point X to point Y within a city using buses in the smallest expected time. Because bus arrival times are not determined by a fixed schedule but instead may be random, the ...

We describe here a simple probabilistic model for graphs that are lifts of a fixed base graph G, i.e., those graphs from which there is a covering man onto G. Our aim is to investigate the properties of typical graphs in this class. In particular, we ...

Let P be a property of graphs. An ∈-test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between ...

We introduce the framework of soft kinetic data structures (SKDS). A soft kinetic data structure is an approximate data structure that can be used to answer queries on a set of moving objects with unpredictable motion. We analyze the quality of a soft ...

Let us consider an ordered vector A[1 : n]. If the cost of testing each position is similar, then the standard binary search is the best strategy to search the vector. This is true in both average and worst case. However, if the costs are non-uniform, ...

We describe several implementations of the kinetic heap, a heap (priority queue) in which the key of each item, instead of being fixed, is a linear function of time. The kinetic heap is a simple example of a kinetic data structure of the kind considered ...

We consider rule sets for internet packet routing and filtering, where each rule consists of a range of source addresses, a range of destination addresses, a priority, and an action. A given packet should be handled by the action from the maximum ...

Dominance constraints are logical tree descriptions originating from automata theory that have multiple applications in computational linguistics. The satisfiability problem of dominance constraints is NP-complete. In most applications, however, only ...

We address the problem of exploring an unknown graph G = (V, E) from a given start node s with either a tethered robot or a robot with a fuel tank of limited capacity, the former being a tighter constraint. In both variations of the problem, the robot ...