Index Catalog // Carleton University Institutional Repository

Resource Type:: Conference Proceeding
Creator:: Markou, Euripides, Kranakis, Evangelos, and Krizanc, Danny
Abstract:: We consider the rendezvous problem for identical mobile agents (i.e., running the same deterministic algorithm) with tokens in a synchronous torus with a sense of direction and show that there is a striking computational difference between one and more tokens. More specifically, we show that 1) two agents with a constant number of unmovable tokens, or with one movable token, each cannot rendezvous if they have o(log n) memory, while they can perform rendezvous with detection as long as they have one unmovable token and O(log n) memory; in contrast, 2) when two agents have two movable tokens each then rendezvous (respectively, rendezvous with detection) is possible with constant memory in an arbitrary n × m (respectively, n × n) torus; and finally, 3) two agents with three movable tokens each and constant memory can perform rendezvous with detection in a n × m torus. This is the first publication in the literature that studies tradeoffs between the number of tokens, memory and knowledge the agents need in order to meet in such a network.
Date Created:: 2006-07-10

Resource Type:: Conference Proceeding
Creator:: Kranakis, Evangelos, Morin, Pat, and Krizanc, Danny
Abstract:: We present a tradeoff between the expected time for two identical agents to rendez-vous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show that there exists a 2t state agent, which can achieve rendez-vous on an n node ring in expected time O( n 2/2 t ∈+∈2 t ) and that any t/2 state agent requires expected time Ω( n 2/2 t ). As a corollary we observe that Θ(loglogn) bits of memory are necessary and sufficient to achieve rendez-vous in linear time.
Date Created:: 2008-05-12

Resource Type:: Conference Proceeding
Creator:: Kranakis, Evangelos, Krizanc, Danny, Narayanan, Lata, and Keane, Michael
Abstract:: Delay (or disruption) tolerant sensor networks may be modeled as Markovian evolving graphs [1]. We present experimental evidence showing that considering multiple (possibly not shortest) paths instead of one fixed (greedy) path can decrease the expected time to deliver a packet on such a network by as much as 65 per cent depending on the probability that an edge exists in a given time interval. We provide theoretical justification for this result by studying a special case of the Markovian evolving grid graph. We analyze a natural algorithm for routing on such networks and show that it is possible to improve the expected time of delivery by up to a factor of two depending upon the probability of an edge being up during a time step and the relative positions of the source and destination. Furthermore we show that this is optimal, i.e., no other algorithm can achieve a better expected running time. As an aside, our results give high probability bounds for Knuth's toilet paper problem [11].
Date Created:: 2009-12-01

Resource Type:: Conference Proceeding
Creator:: Czyzowicz, Jurek, Opatrny, Jaroslav, Kranakis, Evangelos, Narayanan, Lata, Krizanc, Danny, Stacho, Ladislav, Urrutia, Jorge, Yazdani, Mohammadreza, and Lambadaris, Ioannis
Abstract:: A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which establish a barrier coverage of I so that the sum of the distances traveled by all sensors from initial to final positions is minimized. It is shown that the problem is NP complete even to approximate up to constant factor when the sensors may have different sensing ranges. When the sensors have an identical sensing range we give several efficient algorithms to calculate the final destinations so that the sensors either establish a barrier coverage or maximize the coverage of the segment if complete coverage is not feasible while at the same time the sum of the distances traveled by all sensors is minimized. Some open problems are also mentioned.
Date Created:: 2010-12-13

Resource Type:: Conference Proceeding
Creator:: Peleg, David, Krizanc, Danny, Kirousis, Lefteris M., Kranakis, Evangelos, Kaklamanis, Christos, and Bose, Prosenjit
Abstract:: In wireless communication, the signal of a typical broadcast station is transmited from a broadcast center p and reaches objects at a distance, say, R from it. In addition there is a radius r, r < R, such that the signal originating from the center of the station is so strong that human habitation within distance r from the center p should be avoided. Thus every station determines a region which is an “annulus of permissible habitation". We consider the following station layout (SL) problem: Cover a given (say, rectangular) planar region which includes a collection of orthogonal buildings with a minimum number of stations so that every point in the region is within the reach of a station, while at the same time no building is within the dangerous range of a station. We give algorithms for computing such station layouts in both the one-and two-dimensional cases.
Date Created:: 1999-01-01

Resource Type:: Conference Proceeding
Creator:: Krizanc, Danny, Kranakis, Evangelos, and Kirousis, Lefteris M.
Abstract:: Let φ be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number such that if the ratio of the number of clauses over the number of variables of φ strictly exceeds κ, then φ is almost certainly unsatisfiable. By a well known and more or less straightforward argument, it can be shown that κ 3.
Date Created:: 1996-01-01

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