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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 present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (∆ + 1) 2 synchronous communication rounds, where ∆ is the maximum degree of the graph. For ∆ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.
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)
a r t i c l e i n f o a b s t r a c t We give a systematic study of Hamiltonicity of grids — the graphs induced by finite subsets of vertices of the tilings of the plane with congruent regular convex polygons (triangles, squares, or hexagons). Summarizing and extending existing classification of the usual, " square " , grids, we give a comprehensive(More)
In this paper, we study the robust and stochastic versions of the two-stage min-cut 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)
The estimation of the capacity of an airspace region during weather events is an important part of air traffic management. This problem must be solved ahead of time with predicted traffic demands and weather forecasts. In order to capture the uncertainty of the weather, a stochastic weather model is used. We investigate the problem of estimating the maximum(More)
We study the problem of finding shortest non-crossing thick paths in a polygonal domain, where a thick path is the Min-kowski 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)
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 consider the problem of computing k shortest paths in a two-dimensional environment with polygonal obstacles , where the jth path, for 1  j  k, is the shortest path in the free space that is also homotopically distinct from each of the first j 1 paths. In fact, we consider a more general problem: given a source point s, construct a partition of the(More)