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 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:
 Gardezi, Jaffer and Bertossi, Leopoldo
 Abstract:
 Matching Dependencies (MDs) are a recent proposal for declarative entity resolution. They are rules that specify, given the similarities satisfied by values in a database, what values should be considered duplicates, and have to be matched. On the basis of a chaselike procedure for MD enforcement, we can obtain clean (duplicatefree) instances; actually possibly several of them. The clean answers to queries (which we call the resolved answers) are invariant under the resulting class of instances. In this paper, we investigate a query rewriting approach to obtaining the resolved answers (for certain classes of queries and MDs). The rewritten queries are specified in stratified Datalog not,s with aggregation. In addition to the rewriting algorithm, we discuss the semantics of the rewritten queries, and how they could be implemented by means of a DBMS.
 Date Created:
 20121010

 Resource Type:
 Conference Proceeding
 Creator:
 Smid, Michiel, Maheshwari, Anil, Das, Sandip, and Banik, Aritra
 Abstract:
 Let P be a simple polygon with m vertices and let be a set of n points in P. We consider the points of to be users. We consider a game with two players and. In this game, places a point facility inside P, after which places another point facility inside P. We say that a user is served by its nearest facility, where distances are measured by the geodesic distance in P. The objective of each player is to maximize the number of users they serve. We show that for any given placement of a facility by, an optimal placement for can be computed in O(m + n(logn + logm)) time. We also provide a polynomialtime algorithm for computing an optimal placement for.
 Date Created:
 20131008

 Resource Type:
 Conference Proceeding
 Creator:
 Zeh, Norbert, Hutchinson, David, and Maheshwari, Anil
 Abstract:
 We present results related to satisfying shortest path queries on a planar graph stored in external memory. In particular, we show how to store rooted trees in external memory so that bottomup paths can be traversed I/Oefficiently, and we present I/Oefficient algorithms for triangulating planar graphs and computing small separators of such graphs. Using these techniques, we can construct a data structure that allows for answering shortest path queries on a planar graph I/Oefficiently.
 Date Created:
 19990101

 Resource Type:
 Conference Proceeding
 Creator:
 Bose, Prosenjit, Howat, John, and Morin, Pat
 Abstract:
 The time required for a sequence of operations on a data structure is usually measured in terms of the worst possible such sequence. This, however, is often an overestimate of the actual time required. Distributionsensitive data structures attempt to take advantage of underlying patterns in a sequence of operations in order to reduce time complexity, since access patterns are nonrandom in many applications. Unfortunately, many of the distribution sensitive structures in the literature require a great deal of space overhead in the form of pointers. We present a dictionary data structure that makes use of both randomization and existing spaceefficient data structures to yield very low space overhead while maintaining distribution sensitivity in the expected sense.
 Date Created:
 20090914

 Resource Type:
 Conference Proceeding
 Creator:
 Smid, Michiel, Zeh, Norbert, and Maheshwari, Anil
 Abstract:
 We present I/Oefficient algorithms to construct planar Steiner spanners for point sets and sets of polygonal obstacles in the plane, and for constructing the “dumbbell” spanner of [6] for point sets in higher dimensions. As important ingredients to our algorithms, we present I/O efficient algorithms to color the vertices of a graph of bounded degree, answer binary search queries on topology buffer trees, and preprocess a rooted tree for answering prioritized ancestor queries.
 Date Created:
 20010101

 Resource Type:
 Conference Proceeding
 Creator:
 Bose, Prosenjit, Maheshwari, Anil, He, Meng, and Morin, Pat
 Abstract:
 We present a succinct representation of a set of n points on an n×n grid using bits to support orthogonal range counting in time, and range reporting in time, where k is the size of the output. This achieves an improvement on query time by a factor of upon the previous result of Mäkinen and Navarro [1], while using essentially the informationtheoretic minimum space. Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous spaceefficient text indexes that support substring search [2] and positionrestricted substring search [1]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.
 Date Created:
 20090914

 Resource Type:
 Conference Proceeding
 Creator:
 Farshi, Mohammad, Abam, Mohammad Ali, Smid, Michiel, and Carmi, Paz
 Abstract:
 A SemiSeparated Pair Decomposition (SSPD), with parameter s > 1, of a set is a set {(A i ,B i )} of pairs of subsets of S such that for each i, there are balls and containing A i and B i respectively such that min ( radius ) , radius ), and for any two points p, q S there is a unique index i such that p A i and q B i or viceversa. In this paper, we use the SSPD to obtain the following results: First, we consider the construction of geometric tspanners in the context of imprecise points and we prove that any set of n imprecise points, modeled as pairwise disjoint balls, admits a tspanner with edges which can be computed in time. If all balls have the same radius, the number of edges reduces to . Secondly, for a set of n points in the plane, we design a query data structure for halfplane closestpair queries that can be built in time using space and answers a query in time, for any ε> 0. By reducing the preprocessing time to and using space, the query can be answered in time. Moreover, we improve the preprocessing time of an existing axisparallel rectangle closestpair query data structure from quadratic to nearlinear. Finally, we revisit some previously studied problems, namely spanners for complete kpartite graphs and lowdiameter spanners, and show how to use the SSPD to obtain simple algorithms for these problems.
 Date Created:
 20090914

 Resource Type:
 Conference Proceeding
 Creator:
 Smid, Michiel and Gudmundsson, Joachim
 Date Created:
 20130924

 Resource Type:
 Conference Proceeding
 Creator:
 Shi, Wei, Santoro, Nicola, Královič, R., and Dobrev, S.
 Abstract:
 A black hole is a highly harmful host that disposes of visiting agents upon their arrival. It is known that it is possible for a team of mobile agents to locate a black hole in an asynchronous ring network if each node is equipped with a whiteboard of at least O(log n) dedicated bits of storage. In this paper, we consider the less powerful token model: each agent has has available a bounded number of tokens that can be carried, placed on a node or removed from it. All tokens are identical (i.e., indistinguishable) and no other form of communication or coordination is available to the agents. We first of all prove that a team of two agents is sufficient to locate the black hole in finite time even in this weaker coordination model. Furthermore, we prove that this can be accomplished using only O(nlogn) moves in total, which is optimal, the same as with whiteboards. Finally, we show that to achieve this result the agents need to use only O(1) tokens each.
 Date Created:
 20060101