Results 1  10
of
54
MaxMin DCluster Formation in Wireless Ad Hoc Networks
 IN PROCEEDINGS OF IEEE INFOCOM
, 2000
"... An ad hoc network may be logically represented as a set of clusters. The clusterheads form a dhop dominating set. Each node is at most d hops from a clusterhead. Clusterheads form a virtual backbone and may be used to route packets for nodes in their cluster. Previous heuristics restricted themselv ..."
Abstract

Cited by 194 (3 self)
 Add to MetaCart
An ad hoc network may be logically represented as a set of clusters. The clusterheads form a dhop dominating set. Each node is at most d hops from a clusterhead. Clusterheads form a virtual backbone and may be used to route packets for nodes in their cluster. Previous heuristics restricted themselves to 1hop clusters. We show that the minimum dhop dominating set problem is NPcomplete. Then we present a heuristic to form dclusters in a wireless ad hoc network. Nodes are assumed to have nondeterministic mobility pattern. Clusters are formed by diffusing node identities along the wireless links. When the heuristic terminates, a node either becomes a clusterhead, or is at most d wireless hops away from its clusterhead. The value of d is a parameter of the heuristic. The heuristic can be run either at regular intervals, or whenever the network configuration changes. One of the features of the heuristic is that it tends to reelect existing clusterheads even when the network configurat...
Power Consumption in Packet Radio Networks
 THEORETICAL COMPUTER SCIENCE
, 1997
"... In this paper we study the problem of assigning transmission ranges to the nodes of a multihop packet radio network so as to minimize the total power consumed under the constraint that adequate power is provided to the nodes to ensure that the network is strongly connected (i.e., each node can co ..."
Abstract

Cited by 114 (1 self)
 Add to MetaCart
In this paper we study the problem of assigning transmission ranges to the nodes of a multihop packet radio network so as to minimize the total power consumed under the constraint that adequate power is provided to the nodes to ensure that the network is strongly connected (i.e., each node can communicate along some path in the network to every other node). Such assignment of transmission ranges is called complete. We also consider the problem of achieving strongly connected bounded diameter networks.
On the Computational Complexity of Upward and Rectilinear Planarity Testing (Extended Abstract)
, 1994
"... A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical se ..."
Abstract

Cited by 82 (4 self)
 Add to MetaCart
A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment, and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures. In this paper we show that upward planarity testing and rectilinear planarity testing are NPcomplete problems. We also show that it is NPhard to approximate the minimum number of bends in a planar orthogonal drawing of an nvertex graph with an O(n 1\Gammaffl ) error, for any ffl ? 0.
Special Purpose Parallel Computing
 Lectures on Parallel Computation
, 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
Abstract

Cited by 77 (5 self)
 Add to MetaCart
A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...
Separators for spherepackings and nearest neighbor graphs
 J. ACM
, 1997
"... Abstract. A collection of n balls in d dimensions forms a kply system if no point in the space is covered by more than k balls. We show that for every kply system �, there is a sphere S that intersects at most O(k 1/d n 1�1/d) balls of � and divides the remainder of � into two parts: those in the ..."
Abstract

Cited by 74 (7 self)
 Add to MetaCart
Abstract. A collection of n balls in d dimensions forms a kply system if no point in the space is covered by more than k balls. We show that for every kply system �, there is a sphere S that intersects at most O(k 1/d n 1�1/d) balls of � and divides the remainder of � into two parts: those in the interior and those in the exterior of the sphere S, respectively, so that the larger part contains at most (1 � 1/(d � 2))n balls. This bound of O(k 1/d n 1�1/d) is the best possible in both n and k. We also present a simple randomized algorithm to find such a sphere in O(n) time. Our result implies that every knearest neighbor graphs of n points in d dimensions has a separator of size O(k 1/d n 1�1/d). In conjunction with a result of Koebe that every triangulated planar graph is isomorphic to the intersection graph of a diskpacking, our result not only gives a new geometric proof of the planar separator theorem of Lipton and Tarjan, but also generalizes it to higher dimensions. The separator algorithm can be used for point location and geometric divide and conquer in a fixed dimensional space.
Hardness Results for the Power Range Assignment Problem in Packet Radio Networks
 in proceedings of RANDOM/APPROX
, 1999
"... Abstract. The minimum range assignment problem consists of assigning transmission ranges to the stations of a multihop packet radio network so as to minimize the total power consumption provided that the transmission range assigned to the stations ensures the strong connectivity of the network (i.e ..."
Abstract

Cited by 52 (14 self)
 Add to MetaCart
Abstract. The minimum range assignment problem consists of assigning transmission ranges to the stations of a multihop packet radio network so as to minimize the total power consumption provided that the transmission range assigned to the stations ensures the strong connectivity of the network (i.e. each station can communicate with any other station by multihop transmission). The complexity of this optimization problem was studied by Kirousis, Kranakis, Krizanc, and Pelc (1997). In particular, they proved that, when the stations are located in a 3dimensional Euclidean space, the problem is NPhard and admits a 2approximation algorithm. On the other hand, they left the complexity of the 2dimensional case as an open problem. As for the 3dimensional case, we strengthen their negative result by showing that the minimum range assignment problem is APXcomplete, so, it does not admit a polynomialtime approximation scheme unless P=NP. We also solve the open problem discussed by Kirousis et al by proving that the 2dimensional case remains NPhard. 1
Horizons of Parallel Computation
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1993
"... This paper considers the ultimate impact of fundamental physical limitationsnotably, speed of light and device sizeon parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, we take here the provocative view of exploring the ..."
Abstract

Cited by 39 (3 self)
 Add to MetaCart
This paper considers the ultimate impact of fundamental physical limitationsnotably, speed of light and device sizeon parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, we take here the provocative view of exploring the consequences of the accomplished attainment of the physical bounds. The main result is that scalability holds only for neighborly interconnections, such as the square mesh, of boundedsize synchronous modules, presumably of the areauniversal type. We also discuss the ultimate infeasibility of latencyhiding, the violation of intuitive maximal speedups, and the emerging novel processortime tradeoffs.
Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract)
 IN PROC. 2ND ANNU. EUROPEAN SYMPOS. ALGORITHMS
, 1994
"... We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straightline drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on th ..."
Abstract

Cited by 24 (5 self)
 Add to MetaCart
We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straightline drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on the angular resolution of planar straightline drawings, and show a continuous tradeoff between the area and the angular resolution. We also give lineartime algorithms for constructing planar straightline drawings with high angular resolution for various classes of graphs, such as seriesparallel graphs, outerplanar graphs, and triangulations generated by nested triangles. Our results are obtained by new techniques that make extensive use of geometric constructions.
Bubbles: Adaptive Routing Scheme for HighSpeed Dynamic Networks
 SIAM Journal on Computing
, 1997
"... This paper presents the first dynamic routing scheme for highspeed networks. The scheme is based on a hierarchical bubbles partition of the underlying communication graph. ..."
Abstract

Cited by 24 (9 self)
 Add to MetaCart
This paper presents the first dynamic routing scheme for highspeed networks. The scheme is based on a hierarchical bubbles partition of the underlying communication graph.
Optimizing Area and Aspect Ratio in StraightLine Orthogonal Tree Drawings
 Graph Drawing (Proc. GD '96), volume 1190 of Lecture Notes Comput. Sci
, 1997
"... We investigate the problem of drawing an arbitrary nnode binary tree orthogonally in an integer grid using straightline edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In a ..."
Abstract

Cited by 20 (4 self)
 Add to MetaCart
We investigate the problem of drawing an arbitrary nnode binary tree orthogonally in an integer grid using straightline edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call "subtree separation." We investigate both upward and nonupward drawings, achieving area bounds of O(n log n) and O(n log log n), respectively, and we show that, at least in the case of upward drawings, our area bound is optimal to within constant factors.