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We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a(More)
We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless algorithm that works for all(More)
A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queue-number. A three-dimensional (straightline grid) drawing of a graph represents the vertices by points in Z and the edges by(More)
An abstract NP-hard covering problem is presented and xed-parameter tractable algorithms for this problem are described. The running times of the algorithms are expressed in terms of three parameters: n, the number of elements to be covered, k, the number of sets allowed in the covering, and d, the combinatorial dimension of the problem. The rst algorithm(More)
Bloom filters are a randomized data structure for membership queries dating back to 1970. Bloom filters sometimes give erroneous answers to queries, called false positives. Bloom analyzed the probability of such erroneous answers, called the false-positive rate, and Bloom’s analysis has appeared in many publications throughout the years. We show that(More)
We present a succinct representation of a set of n points on an n × n grid using n lg n + o(n lg n) bits to support orthogonal range counting in O(lg n/ lg lg n) time, and range reporting in O(k lg n/ lg lg n) time, where k is the size of the output. This achieves an improvement on query time by a factor of lg lg n upon the previous result of Mäkinen and(More)
We consider cuckoo hashing as proposed by Pagh and Rodler in 2001. We show that the expected construction time of the hash table is O(n) as long as the two open addressing tables are each of size at least (1 + ǫ)n, where ǫ > 0 and n is the number of data points. Slightly improved bounds are obtained for various probabilities and constraints. The analysis(More)
Supporting nodes without Global Positioning System (GPS) capability, in wireless ad hoc and sensor networks, has numerous applications in guidance and surveying systems in use today. At issue is that a procedure be available so that the subset of nodes with GPS capability succeed in supporting the maximum possible number of nodes without GPS capability and(More)