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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. ..."
Abstract

Cited by 15 (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.
Graph Drawing
 Lecture Notes in Computer Science
, 1997
"... INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computeraideddesign. Research on graph drawing has been conducte ..."
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Cited by 14 (3 self)
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INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computeraideddesign. Research on graph drawing has been conducted within several diverse areas, including discrete mathematics (topological graph theory, geometric graph theory, order theory), algorithmics (graph algorithms, data structures, computational geometry, vlsi), and humancomputer interaction (visual languages, graphical user interfaces, software visualization). This chapter overviews aspects of graph drawing that are especially relevant to computational geometry. Basic definitions on drawings and their properties are given in Section 1.1. Bounds on geometric and topological properties of drawings (e.g., area and crossings) are presented in Section 1.2. Section 1.3 deals with the time complexity of fundamental graph drawin
Advances in the Theory and Practice of Graph Drawing
 Theor. Comp. Sci
, 1996
"... The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph d ..."
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Cited by 4 (0 self)
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The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph drawing. Specific topics include bounds and tradeoffs for drawing properties, threedimensional representations, methods for constraint satisfaction, and experimental studies. 1 Introduction In this paper, we survey selected research trends in graph drawing, and overview some recent results of the author and his collaborators. Graph drawing addresses the problem of constructing geometric representations of graphs, a key component of support tools for complex applications in science and engineering. Graph drawing is a young research field that has growth very rapidly in the last decade. One of its distinctive characteristics is to have furthered collaborative efforts between computer scien...