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 Resource Type:
 Conference Proceeding
 Creator:
 Nayak, Amiya, Du, Jingzhe, and Kranakis, Evangelos
 Abstract:
 We describe a novel Distributed Storage protocol in Disruption (Delay) Tolerant Networks (DTN). Since DTNs can not guarantee the connectivity of the network all the time, distributed data storage and look up has to be performed in a storeandforward way. In this work, we define local distributed location regions which are called cells to facilitate the data storage and look up process. Nodes in a cell have high probability of moving within their cells. Our protocol resorts to storing data items in cells which have hierarchical structure to reduce routing information storage at nodes. Multiple copies of a data item may be stored at nodes to counter the adverse impact of the nature of DTNs. The cells are relatively stable regions and as a result, data exchange overheads among nodes are reduced. Through experimentation, we show that the proposed distributed storage protocol achieves higher successful data storage ratios with lower delays and limited data item exchange requirements than other protocols in the literature.
 Date Created:
 20100827

 Resource Type:
 Conference Proceeding
 Creator:
 Kranakis, Evangelos, Pelc, Andrzej, and Paquette, Michel
 Abstract:
 We study the feasibility and time of communication in random geometric radio networks, where nodes fail randomly with positive correlation. We consider a set of radio stations with the same communication range, distributed in a random uniform way on a unit square region. In order to capture fault dependencies, we introduce the ranged spot model in which damaging events, called spots, occur randomly and independently on the region, causing faults in all nodes located within distance s from them. Node faults within distance 2s become dependent in this model and are positively correlated. We investigate the impact of the spot arrival rate on the feasibility and the time of communication in the faultfree part of the network. We provide an algorithm which broadcasts correctly with probability 1  ε in faulty random geometric radio networks of diameter D in time O(D + log1/ε).
 Date Created:
 20081126

 Resource Type:
 Conference Proceeding
 Creator:
 Wiese, Andreas and Kranakis, Evangelos
 Date Created:
 20081126

 Resource Type:
 Conference Proceeding
 Creator:
 Ponce, Oscar Morales, Pacheco, Eduardo, Kranakis, Evangelos, Ga̧sieniec, Leszek, Czyzowicz, Jurek, and Kosowski, Adrian
 Abstract:
 A collection of n anonymous mobile robots is deployed on a unitperimeter ring or a unitlength line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing. Each robot has a clock allowing it to observe the times of its bounces. The robots have no control on their walks, which are determined by their initial positions and the starting directions. Each robot executes the same position detection algorithm, which receives input data in realtime about the times of the bounces, and terminates when the robot is assured about the existence and the positions of all the robots. Some initial configuration of robots are shown to be infeasible  no position detection algorithm exists for them. We give complete characterizations of all infeasible initial configurations for both the ring and the segment, and we design optimal position detection algorithms for all feasible configurations. For the case of the ring, we show that all robot configurations in which not all the robots have the same initial direction are feasible. We give a position detection algorithm working for all feasible configurations. The cost of our algorithm depends on the number of robots starting their movement in each direction. If the less frequently used initial direction is given to k ≤ n/2 robots, the time until completion of the algorithm by the last robot is 1/2 ⌈n/k⌉. We prove that this time is optimal. By contrast to the case of the ring, for the unit segment we show that the family of infeasible configurations is exactly the set of socalled symmetric configurations. We give a position detection algorithm which works for all feasible configurations on the segment in time 2, and this algorithm is also proven to be optimal.
 Date Created:
 20121109

 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:
 20060710

 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 rendezvous 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 rendezvous 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 rendezvous in linear time.
 Date Created:
 20080512

 Resource Type:
 Conference Proceeding
 Creator:
 Kranakis, Evangelos and Wiese, Andreas
 Abstract:
 We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geographic coordinates in the plane (location aware nodes). Our algorithms are local in the sense that the status of each node v (whether or not v is in the computed set) depends only on the vertices which are a constant number of hops away from v. This constant is independent of the size of the network. We give upper bounds for the constant depending on the desired approximation ratio. We show that the processing time which is necessary in order to compute the status of a single vertex is bounded by a polynomial in the number of vertices which are at most a constant number of vertices away from it. Our algorithms give the best possible approximation ratios for this setting. The technique which we use to obtain the algorithm for vertex cover can also be employed for constructing the first global PTAS for this problem in unit disk graph which does not need the embedding of the graph as part of the input.
 Date Created:
 20080701

 Resource Type:
 Conference Proceeding
 Creator:
 Kranakis, Evangelos, Shi, Q., Bhattacharya, B., Wiese, A., Burmester, B., and Hu, Y.
 Abstract:
 Intrusion detection, area coverage and border surveillance are important applications of wireless sensor networks today. They can be (and are being) used to monitor large unprotected areas so as to detect intruders as they cross a border or as they penetrate a protected area. We consider the problem of how to optimally move mobile sensors to the fence (perimeter) of a region delimited by a simple polygon in order to detect intruders from either entering its interior or exiting from it. We discuss several related issues and problems, propose two models, provide algorithms and analyze their optimal mobility behavior.
 Date Created:
 20080922

 Resource Type:
 Conference Proceeding
 Creator:
 Kranakis, Evangelos and Wiese, Andreas
 Abstract:
 We investigate the problem of locally coloring and constructing special spanners of location aware Unit Disk Graphs (UDGs). First we present a local approximation algorithm for the vertex coloring problem in UDGs which uses at most four times as many colors as required by an optimal solution. Then we look at the colorability of spanners of UDGs. In particular we present a local algorithm for constructing a 4colorable spanner of a unit disk graph. The output consists of the spanner and the 4coloring. The computed spanner also has the properties that it is planar, the degree of a vertex in the spanner is at most 5 and the angles between two edges are at least π/3. By enlarging the locality distance (i.e. the size of the neighborhood which a vertex has to explore in order to compute its color) we can ensure the total weight of the spanner to be arbitrarily close to the weight of a minimum spanning tree. We prove that a local algorithm cannot compute a bipartite spanner of a unit disk graph and therefore our algorithm needs at most one color more than any local algorithm for the task requires. Moreover, we prove that there is no local algorithm for 3coloring UDGs or spanners of UDGs, even if the 3colorability of the graph (or the spanner respectively) is guaranteed in advance.
 Date Created:
 20081201

 Resource Type:
 Conference Proceeding
 Creator:
 Krizanc, D., Yazdani, M., Stacho, L., Narayanan, L., Lambadaris, Ioannis, Opatrny, J., Czyzowicz, J., Kranakis, Evangelos, and Urrutia, J.
 Abstract:
 We consider n mobile sensors located on a line containing a barrier represented by a finite line segment. Sensors form a wireless sensor network and are able to move within the line. An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor. The sensor network establishes barrier coverage of the segment if no intruder can penetrate the barrier from any direction in the plane without being detected. Starting from arbitrary initial positions of sensors on the line we are interested in finding final positions of sensors that establish barrier coverage and minimize the maximum distance traversed by any sensor. We distinguish several variants of the problem, based on (a) whether or not the sensors have identical ranges, (b) whether or not complete coverage is possible and (c) in the case when complete coverage is impossible, whether or not the maximal coverage is required to be contiguous. For the case of n sensors with identical range, when complete coverage is impossible, we give linear time optimal algorithms that achieve maximal coverage, both for the contiguous and noncontiguous case. When complete coverage is possible, we give an O(n 2) algorithm for an optimal solution, a linear time approximation scheme with approximation factor 2, and a (1∈+∈ε) PTAS. When the sensors have unequal ranges we show that a variation of the problem is NPcomplete and identify some instances which can be solved with our algorithms for sensors with unequal ranges.
 Date Created:
 20091019