Results 1  10
of
45
Routing with Guaranteed Delivery in ad hoc Wireless Networks
 WIRELESS NETWORKS
, 2001
"... 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 ..."
Abstract

Cited by 648 (74 self)
 Add to MetaCart
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 packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A byproduct of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms.
Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
Abstract

Cited by 560 (5 self)
 Add to MetaCart
This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.
Geographic routing made practical
, 2005
"... Geographic routing has been widely hailed as the most promising approach to generally scalable wireless routing. However, the correctness of all currently proposed geographic routing algorithms relies on idealized assumptions about radios and their resulting connectivity graphs. We use testbed measu ..."
Abstract

Cited by 136 (4 self)
 Add to MetaCart
Geographic routing has been widely hailed as the most promising approach to generally scalable wireless routing. However, the correctness of all currently proposed geographic routing algorithms relies on idealized assumptions about radios and their resulting connectivity graphs. We use testbed measurements to show that these idealized assumptions are grossly violated by real radios, and that these violations cause persistent failures in geographic routing, even on static topologies. Having identified this problem, we then fix it by proposing the CrossLink Detection Protocol (CLDP), which enables provably correct geographic routing on arbitrary connectivity graphs. We confirm in simulation and further testbed measurements that CLDP is not only correct but practical: it incurs low overhead, exhibits low path stretch, always succeeds in real, static wireless networks, and converges quickly after topology changes. 1
Coverage in Wireless Adhoc Sensor Networks
, 2002
"... Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this pape ..."
Abstract

Cited by 113 (9 self)
 Add to MetaCart
Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the bestcoverage problem raised in [1]. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum bestcoverage path with the least energy consumption. We also consider how to find an optimum bestcoveragepath that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.
Greedy optimal homotopy and homology generators
 Proc. 16th Ann. ACMSIAM Symp. Discrete Algorithms
, 2005
"... Abstract We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2manifold. In particular, we show that the shortest set of loops t ..."
Abstract

Cited by 88 (12 self)
 Add to MetaCart
Abstract We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2manifold. In particular, we show that the shortest set of loops that generate the fundamental group of any oriented combinatorial 2manifold, with any given basepoint, can be constructed in O(n log n) time using a straightforward application of Dijkstra's shortest path algorithm. This solves an open problem of Colin de Verdi`ere and Lazarus.
Shapes And Implementations In ThreeDimensional Geometry
, 1993
"... Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in th ..."
Abstract

Cited by 37 (5 self)
 Add to MetaCart
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three dimensional space. Each shape is a welldefined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case.
On the Spanning Ratio of Gabriel Graphs and βSkeletons
, 2001
"... The spanning ratio of a graph de ned on n points in the Euclidean plane is the maximal ratio over all pairs of data points (u; v), of the minimum graph distance between u and v, over the Euclidean distance between u and v. A connected graph is said to be a kspanner if the spanning ratio does n ..."
Abstract

Cited by 36 (0 self)
 Add to MetaCart
The spanning ratio of a graph de ned on n points in the Euclidean plane is the maximal ratio over all pairs of data points (u; v), of the minimum graph distance between u and v, over the Euclidean distance between u and v. A connected graph is said to be a kspanner if the spanning ratio does not exceed k. For example, for any k, there exists a point set whose minimum spanning tree is not a kspanner. At the other end of the spectrum, a Delaunay triangulation is guaranteed to be a 2:42spanner [11]. For proximity graphs inbetween these two extremes, such as Gabriel graphs[8], relative neighborhood graphs[16] and skeletons[12] with 2 [0; 2] some interesting questions arise. We show that the spanning ratio for Gabriel graphs (which are skeletons with = 1) is ( in the worst case. For all skeletons with 2 [0; 1], we prove that the spanning ratio is at most O(n ) where = (1 log 2 (1 + ))=2.
Competitive Online Routing in Geometric Graphs
 Theoretical Computer Science
, 2001
"... We consider online routing algorithms for finding paths between the vertices of plane graphs. ..."
Abstract

Cited by 34 (4 self)
 Add to MetaCart
We consider online routing algorithms for finding paths between the vertices of plane graphs.