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Constantdegree graph expansions that preserve treewidth
"... Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomialtime upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical conce ..."
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Cited by 2 (0 self)
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question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G = (V,E) admits an expansion G ′ = (V ′,E ′ ) with the maximum degree ≤ 3 and treewidth
Randomness conductors and the constantdegree expansions . . .
, 2001
"... The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: ¤¦¥¨§�©��� � , where � is the degree and © is an arbitrarily small constant. Such graphs are essential components in ..."
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Cited by 33 (2 self)
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The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: ¤¦¥¨§�©��� � , where � is the degree and © is an arbitrarily small constant. Such graphs are essential components
Randomness Conductors and ConstantDegree LosslessExpanders
"... ABSTRACT The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 s^)D, where D is the degree and s ^ is an arbitrarily small constant. The best previous explicit constru ..."
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ABSTRACT The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 s^)D, where D is the degree and s ^ is an arbitrarily small constant. The best previous explicit
Domino treewidth
 DISCRETE MATH. THEOR. COMPUT. SCI
, 1994
"... We consider a special variant of treedecompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino treedecomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck;d such that ..."
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Cited by 86 (4 self)
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We consider a special variant of treedecompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino treedecomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck
Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes
, 2002
"... In this paper, we present a onetoone embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a highly irregular structure into hypercubes are investigated. The presented embedding achieves dilation of at most 3�log��d + 1��t + 1 ..."
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Cited by 1 (0 self)
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, the embedding of a graph with constant treewidth and constant degree can be computed in time O�log 2 �n � log log log�n � log ∗ �n��. For graphs with constant treewidth, a minimal treedecomposition can be computed efficiently in parallel due to a result of Bodlaender and Hagerup. In this case, the embedding
Bandwidth, treewidth, separators, expansion, and universality
"... We prove that planar graphs with bounded maximum degree have sublinear bandwidth. As a consequence for each γ> 0 every nvertex graph with minimum degree (3 4 + γ)n contains a copy of every boundeddegree planar graph on n vertices. The proof relies on the fact that planar graphs have small sepa ..."
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separators. Indeed, we show more generally that for any class of boundeddegree graphs the concepts of sublinear bandwidth, sublinear treewidth, the absence of big expanders as subgraphs, and the existence of small separators are equivalent.
I/Oefficient algorithms for bounded treewidth graphs
 In Proc. ACMSIAM Symp. on Discrete Algorithms
, 2001
"... We present an I/Oefficient algorithm for the single source shortest path (SSSP) problem for graphs of bounded treewidth. For sparse graphs in general SSSP seems to be extremely hard to solve. We show how to solve SSSP in O sort N¡¢ ¡ I/Os for the above class of graphs. An important ingredient t ..."
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Cited by 1 (0 self)
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We present an I/Oefficient algorithm for the single source shortest path (SSSP) problem for graphs of bounded treewidth. For sparse graphs in general SSSP seems to be extremely hard to solve. We show how to solve SSSP in O sort N¡¢ ¡ I/Os for the above class of graphs. An important ingredient
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Algorithms for Graphs of (Locally) Bounded Treewidth
, 2001
"... Many reallife problems can be modeled by graphtheoretic problems. These graph problems are usually NPhard and hence there is no efficient algorithm for solving them, unless P= NP. One way to overcome this hardness is to solve the problems when restricted to special graphs. Trees are one kind of g ..."
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Cited by 4 (3 self)
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of graph for which several NPcomplete problems can be solved in polynomial time. Graphs of bounded treewidth, which generalize trees, show good algorithmic properties similar to those of trees. Using ideas developed for tree algorithms, Arnborg and Proskurowski introduced a general dynamic programming
Results 1  10
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