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Orderly Spanning Trees with Applications to Graph Encoding and Graph Drawing
 In 12 th Symposium on Discrete Algorithms (SODA
, 2001
"... The canonical ordering for triconnected planar graphs is a powerful method for designing graph algorithms. This paper introduces the orderly pair of connected planar graphs, which extends the concept of canonical ordering to planar graphs not required to be triconnected. Let G be a connected planar ..."
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Cited by 34 (6 self)
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The canonical ordering for triconnected planar graphs is a powerful method for designing graph algorithms. This paper introduces the orderly pair of connected planar graphs, which extends the concept of canonical ordering to planar graphs not required to be triconnected. Let G be a connected planar graph. We give a lineartime algorithm that obtains an orderly pair (H
Orderly Spanning Trees with Applications
 SIAM Journal on Computing
, 2005
"... Abstract. We introduce and study orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any c ..."
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Cited by 11 (1 self)
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Abstract. We introduce and study orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any connected planar graph G, consisting of an embedded planar graph H isomorphic to G, and an orderly spanning tree of H. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyderâ€™s realizer theorem, (2) the first algorithm for computing an areaoptimal 2visibility drawing of a planar graph, and (3) the most compact known encoding of a planar graph with O(1)time query support. All algorithms in this paper run in linear time.
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For ..."
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Cited by 11 (2 self)
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A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
Undirected VertexConnectivity Structure and Smallest FourVertexConnectivity Augmentation
 Proc. 6th ISAAC
, 1995
"... In this paper, we study properties for the structure of an undirected graph that is not 4vertexconnected. We also study the evolution of this structure when an edge is added to optimally increase the vertexconnectivity of the underlying graph. Several properties reported here can be extended t ..."
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Cited by 4 (0 self)
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In this paper, we study properties for the structure of an undirected graph that is not 4vertexconnected. We also study the evolution of this structure when an edge is added to optimally increase the vertexconnectivity of the underlying graph. Several properties reported here can be extended to the case of a graph that is not kvertex connected, for an arbitrary k. Using properties obtained here, we solve the problem of finding a smallest set of edges whose addition 4vertexconnects an undirected graph. This is a fundamental problem in graph theory and has applications in network reliability and in statistical data security. We give an O(n \Delta log n + m)time algorithm for finding a set of edges with the smallest cardinality whose addition 4vertexconnects an undirected graph, where n and m are the number of vertices and edges in the input graph, respectively. This is the first polynomial time algorithm for this problem when the input graph is not 3vertexconnecte...
Blind Queries to XML Data
, 2000
"... . A flexible query model is presented for wellformed XML documents. Our approach relies on modeling XML documents as labeled graphs and selectively extending their structure by computing fuzzy estimates of the importance of the information they provide, at the granularity of XML tags. The resul ..."
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Cited by 1 (0 self)
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. A flexible query model is presented for wellformed XML documents. Our approach relies on modeling XML documents as labeled graphs and selectively extending their structure by computing fuzzy estimates of the importance of the information they provide, at the granularity of XML tags. The result of such an extension is a fuzzy labeled graph. Query results are subgraphs of this fuzzy labeled graph, presented as a ranked list according to their degree of matching to the user query. 1 Introduction and Motivations XML (eXtensible Markup Language) is a markup metalanguage designed to enable semanticsaware tagging of World Wide Web information [XML]. Generally speaking, an XML document is composed of a sequence of nested elements, each delimited by a pair of start and end tags (e.g., !tag? and !/tag?). An XML document is wellformed if it obeys the basic syntax of XML (e.g., nonempty tags are properly nested, each nonempty start tag have the corresponding end tag). Wellformed do...