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Results 1 - 10
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358
Minimum-energy broadcast in allwireless networks: Np-completeness and distribution
- In Proc. of ACM MobiCom
, 2002
"... In all-wireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consump ..."
Abstract
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Cited by 177 (2 self)
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consumption. Several authors have conjectured that the problem of power-optimal broadcast is NP-complete. We provide here a formal proof, both for the general case and for the geometric one; in the former case, the network topology is represented by a generic graph with arbitrary weights, whereas
The Number of Embeddings of Minimally Rigid Graphs
- GEOMETRY © 2003 SPRINGER-VERLAG NEW YORK INC.
, 2003
"... Rigid frameworks in some Euclidean space are embedded graphs having a unique local realization (up to Euclidean motions) for the given edge lengths, although globally they may have several. We study the number of distinct planar embeddings of minimally rigid graphs with n vertices. We show that, mo ..."
Abstract
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Cited by 15 (2 self)
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Rigid frameworks in some Euclidean space are embedded graphs having a unique local realization (up to Euclidean motions) for the given edge lengths, although globally they may have several. We study the number of distinct planar embeddings of minimally rigid graphs with n vertices. We show that
Planar embedding of planar graphs
- Advances in Computing Research
, 1984
"... Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI theory. Valiant [12] gave an algorithm to construct a planar embedding for trees in linear area, he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Va ..."
Abstract
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Cited by 31 (1 self)
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Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI theory. Valiant [12] gave an algorithm to construct a planar embedding for trees in linear area, he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between
Proximity Preservation and Crossing-Minimization for Graph Embedding
"... We propose a novel approach to embedding heterogeneous data in high-dimensional space characterized by a graph. Targeted towards data visualization, the objectives of the embedding are two-fold: (i) preserve proximity relations as measured by some embedding objective, and (ii) simultaneously optimiz ..."
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pairwise distances and Euclidean distances in the embedding for all nodes. However, layouts that preserve proximity relations can have a large number of edge-crossings obfuscating the relationships between nodes making the graph dicult to understand and interpret. It is therefore desir-able to minimize
NP-Completeness for Minimizing Maximum Edge . . .
, 1985
"... Given an embedding f: G-+ 2 of a graph G in the two-dimensional lattice, let Iff be the maximum L 1 distance between points f(x) and f(y) where xy is an edge of G. Let B 2 ( G) be the minimum Ifl over all embeddings f. It is shown that the determination of B 2 ( G) for arbitrary G is NP-complete. Es ..."
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Given an embedding f: G-+ 2 of a graph G in the two-dimensional lattice, let Iff be the maximum L 1 distance between points f(x) and f(y) where xy is an edge of G. Let B 2 ( G) be the minimum Ifl over all embeddings f. It is shown that the determination of B 2 ( G) for arbitrary G is NP-complete
A Note on Embedding Complete Graphs into Hypercubes
, 1995
"... An embedding of K n into a hypercube is a mapping of the n vertices of K n to distinct vertices of the hypercube, and the associated cost is the sum over all pairs of (mapped) vertices of the Hamming distance between the vertices. Let f(n) denote the minimum cost over all embeddings of K n into a hy ..."
Abstract
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An embedding of K n into a hypercube is a mapping of the n vertices of K n to distinct vertices of the hypercube, and the associated cost is the sum over all pairs of (mapped) vertices of the Hamming distance between the vertices. Let f(n) denote the minimum cost over all embeddings of K n into a
Minimal Euclidean representations of graphs
, 2009
"... A simple graph G is representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct values α or β, with distance α if the vertices are adjacent and distan ..."
Abstract
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Cited by 1 (0 self)
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A simple graph G is representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct values α or β, with distance α if the vertices are adjacent
Testing Planarity of Partially Embedded Graphs
, 2009
"... We study the following problem: Given a planar graph G and a planar drawing (embedding) of a subgraph of G, can such a drawing be extended to a planar drawing of the entire graph G? This problem fits the paradigm of extending a partial solution to a complete one, which has been studied before in man ..."
Abstract
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Cited by 23 (10 self)
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We study the following problem: Given a planar graph G and a planar drawing (embedding) of a subgraph of G, can such a drawing be extended to a planar drawing of the entire graph G? This problem fits the paradigm of extending a partial solution to a complete one, which has been studied before
Low-density MDS codes and factors of complete graphs
- INFORMATION THEORY, IEEE TRANSACTIONS ON
, 1999
"... We present a class of array code of size n 2 l, where l = 2nor 2n +1, called B-Code. The distances of the B-Code and its dual are 3 and l 0 1, respectively. The B-Code and its dual are optimal in the sense that i) they are maximum-distance separable (MDS), ii) they have an optimal encoding property ..."
Abstract
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Cited by 36 (9 self)
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property, i.e., the number of the parity bits that are affected by change of a single information bit is minimal, and iii) they have optimal length. Using a new graph description of the codes, we prove an equivalence relation between the construction of the B-Code (or its dual) and a combinatorial problem
Results 1 - 10
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358
