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An Efficient Algorithm for the VertexDisjoint Paths Problem in Random Graphs
, 1996
"... Given a graph G = (V, E) and a set of pairs of vertices in V, we are interested in finding for each pair (ui, b;) a path connecting ai to bi, such that the set of paths so found is vertexdisjoint, (The problem is M/Pcomplete for general graphs as well as for planar graphs. It is in P if the number ..."
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Cited by 4 (0 self)
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Given a graph G = (V, E) and a set of pairs of vertices in V, we are interested in finding for each pair (ui, b;) a path connecting ai to bi, such that the set of paths so found is vertexdisjoint, (The problem is M/Pcomplete for general graphs as well as for planar graphs. It is in P
GREW—A Scalable Frequent Subgraph Discovery Algorithm
 in Fourth IEEE International Conference on Data Mining (ICDM 2004). 2004
, 2003
"... Existing algorithms that mine graph datasets to discover patterns corresponding to frequently occurring subgraphs can operate efficiently on graphs that are sparse, contain a large number of relatively small connected components, have vertices with low and bounded degrees, and contain welllabeled v ..."
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Cited by 21 (0 self)
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subgraph discovery algorithms. GREW is designed to operate on a large graph and to find patterns corresponding to connected subgraphs that have a large number of vertexdisjoint embeddings. Our experimental evaluation shows that GREW is efficient, can scale to very large graphs, and find non
On Embedding an OuterPlanar Graph in a Point Set
 CGTA: Computational Geometry: Theory and Applications
, 1997
"... Given an nvertex outerplanar graph G and a set P of n points in the plane, we present an O(n log n) time and O(n) space algorithm to compute a straightline embedding of G in P , improving upon the algorithm in [GMPP91, CU96] that requires O(n ) time. Our algorithm is nearoptimal as the ..."
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Cited by 45 (1 self)
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optimal as there is an\Omega (n log n) lower bound for the problem [BMS95]. We present a simpler O(nd) time and O(n) space algorithm to compute a straightline embedding of G in P where log n d 2n is the length of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler
Embedding Starlike Trees into HypercubeLike Interconnection Networks
"... Abstract. A starlike tree (or a quasistar) is a subdivision of a star tree. A family of hypercubelike interconnection networks called restricted HLgraphs includes many interconnection networks proposed in the literature such as twisted cubes, crossed cubes, multiply twisted cubes, Möbius cubes, Mcu ..."
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, Mcubes, and generalized twisted cubes. We show in this paper that every starlike tree of degree at most m with 2 m vertices is a spanning tree of mdimensional restricted HLgraphs. It is also proved that in an mdimensional restricted HLgraph, there exist k( ≤ m − 1) vertexdisjoint sipaths with li
Časopis pro pěstování matematiky * roč. 104 (1979), Praha EMBEDDING TREES INTO CLIQUEBRIDGECLIQUE GRAPHS
, 1977
"... The paper [2] concerns embedding trees into graphs which have exactly two blocks, each of them being a clique. Now we shall study a similar problem — embedding trees into graphs which consist of two vertexdisjoint cliques and of a bridge between them. Such a graph will be called a cliquebridgecli ..."
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The paper [2] concerns embedding trees into graphs which have exactly two blocks, each of them being a clique. Now we shall study a similar problem — embedding trees into graphs which consist of two vertexdisjoint cliques and of a bridge between them. Such a graph will be called a clique
ManhattanGeodesic Embedding of Planar Graphs
"... In this paper, we explore a new convention for drawing graphs, the (Manhattan) geodesic drawing convention. It requires that edges are drawn as interiordisjoint monotone chains of axisparallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic ..."
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Cited by 9 (2 self)
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In this paper, we explore a new convention for drawing graphs, the (Manhattan) geodesic drawing convention. It requires that edges are drawn as interiordisjoint monotone chains of axisparallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic
Annular embeddings of permutations for arbitrary genus
, 2008
"... In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each disjoint cycle has length 2). Harer and Zagier explicitly determined the distribution of the number of disjoint cycles in the ..."
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Cited by 2 (0 self)
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in the product of a fixed cycle of length 2n and the elements of P2n. Their famous result has been reproved many times, primarily because it can be interpreted as the genus distribution for 2cell embeddings in an orientable surface, of a graph with a single vertex attached to n loops. In this paper we give a
Graphs with (Edge) Disjoint Links in Every Spatial Embedding
, 1999
"... We describe some characteristics of graphs with (edge) disjoint pairs of links in every spatial embedding. In particular, we showthe smallest complete graphs that contain pairs of nonsplittable links in every spatial embedding that share no edges is K 7 .Further we find a large set of minimal ..."
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Cited by 2 (0 self)
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graphs that have pairs of nonsplittable links sharing no vertices or edges in every spatial embedding. We show that \DeltaY exchanges and vertex splittings are disjoint link preserving operations. We find regular graphs of arbitrarily high genus that have a linkless embedding. We conjecture
Tree Embeddings for TwoEdgeConnected Network Design
"... The group Steiner problem is a classical network design problem where we are given a graph and a collection of groups of vertices, and want to build a mincost subgraph that connects the root vertex to at least one vertex from each group. What if we wanted to build a subgraph that twoedgeconnects ..."
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Cited by 5 (1 self)
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edgeconnects the root to each group—that is, for every group g ⊆ V, the subgraph should contain two edgedisjoint paths from the root to some vertex in g? What if we wanted the two edgedisjoint paths to end up at distinct vertices in the group, so that the loss of a single member of the group would not destroy
Optimal Dynamic EdgeDisjoint Embeddings of Complete Binary Trees into Hypercubes
, 1996
"... The doublerooted complete binary tree is a complete binary tree where the path (of 2 length2) between the children of the root is replaced by a path of length3. It is folklore that the doublerooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual ..."
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trees into hypercubes which do not suffer from this disadvantage. We also give an edgedisjoint embedding with optimal load2and unit dilation such that each hypercube vertex is an image of at most one vertex of a level. Moreover, these embeddings can be efficiently implemented on the hypercube itself
Results 1  10
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46