Valentin Polishchuk

Learn More
In the relay placement problem, the input is a set of sensors and a number <i>r</i> &ges; 1, the communication range of a relay. In the <i>one-tier</i> version of the problem, the objective is to place a minimum number of relays so that between every pair of sensors there is a path <i>through sensors and/or relays</i> such that the consecutive vertices of(More)
We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its(More)
We consider instances of the Stable Roommates problem that arise from geometric representation of participants preferences: a participant is a point in a metric space, and his preference list is given by sorted distances to the other participants. We observe that, unlike in the general case, if there are no ties in the preference lists, there always exists(More)
In this paper, we study strategies for allocating and managing friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i) protecting the privacy of storage locations where RFID(More)
We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the(More)
We study the problem of finding shortest non-crossing thick paths in a polygonal domain, where a thick path is the Minkowski sum of a usual (zero-thickness, or thin) path and a disk. Given K pairs of terminals on the boundary of a simple n-gon, we compute in O(n + K) time a representation of the set of K shortest non-crossing thick paths joining the(More)
Given a graph G = (V , E), a subset of nodes C ⊆ V is a vertex cover if each edge {u, v} ∈ E has u ∈ C or v ∈ C . In this work, we present a constant-time distributed algorithm for finding a factor 3 approximation for minimum vertex cover in bounded-degree graphs. A distributed algorithm that runs in constant time (constant number of synchronous(More)
We study the problem of finding a shortest tour visiting a given sequence of convex bodies in R. To our knowledge, this is the first attempt to attack the problem in its full generality: we investigate high-dimensional cases (d ≥ 2); we consider convex bodies bounded by (hyper)planes and/or (hyper)spheres; we do not restrict the start and the goal positions(More)
In this paper, we study the robust and stochastic versions of the two-stage mincut and shortest path problems introduced in Dhamdhere et al. [6], and give approximation algorithms with improved approximation factors. Specifically, we give a 2-approximation for the robust min-cut problem and a 4-approximation for the stochastic version. For the two-stage(More)