Article history: Received 20 December 2012 Received in revised form 12 December 2013 Accepted 14 January 2014 Communicated by R. van Glabbeek

Given a set S = {P1, . . . , Pn} of n points in R, the depth δ(Q) of a point Q ∈ R is the minimum number of points of S that must be in a closed halfspace containing Q. A high depth point is a point whose depth is at least maxi [δ(Pi)]. For dimension d = 2 we give a simple, easily implementable O(n(log n)) deterministic algorithm to compute a high depth point and we give an Ω(n log n) lower bou...

Given a finite alphabet Σ and a deterministic finite automaton on Σ, the problem of determining whether the language recognized by the automaton contains any pangram is NP-complete.

We consider the design of an optimal mechanism for a seller selling two items to a single buyer so that the expected revenue to the seller is maximized. The buyer’s valuation of the two items is assumed to be the uniform distribution over an arbitrary rectangle [c1, c1 + b1] × [c2, c2 + b2] in the positive quadrant. The solution to the case when (c1, c2) = (0, 0) was already known. We provide a...

We investigate weak recognizability of deterministic languages of infinite trees. We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, we propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states. The algorithm works within the time of solving the emptiness...

We analyze the routing of k-permutations on circular processor arrays connected by bidirectional links. In contrast to linear processor arrays, it is hard to prove lower bounds for the routing time or to construct eecient algorithms for routing k-permutations on circular arrays (except for the case k = 1). We will prove non-trivial lower bounds for routing with global knowledge and for routing ...

A two-way finite automaton is sweeping if its input head can change direction only on the end-markers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n)-state sweeping LasVegas automaton, but needs 2 states on every sweeping deterministic automaton.

Optimal randomized and deterministic algorithms have been given for k-k routing on two-dimensional n n meshes. The deterministic algorithm is based on “column-sort” and exploits only part of the features of the mesh. For small n and moderate k, the lower-order terms of this algorithm make it considerably more expensive than the randomized algorithm. In this paper, we present a novel determinist...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...