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76
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
Abstract

Cited by 544 (40 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
A Unified Framework and Algorithm for Channel Assignment
 in Wireless Networksâ€ť, Wireless Networks, Volume 5, Issue 2
, 1999
"... Channel assignment problems in the time, frequency and code domains have thus far been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framew ..."
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Cited by 123 (0 self)
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Channel assignment problems in the time, frequency and code domains have thus far been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framework identifies eleven atomic constraints underlying most current and potential assignment problems, and characterizes a problem as a combination of these constraints. Based on this framework, we present a unified algorithm for efficient (T/F/C)DMA channel assignments to network nodes or to internodal links in a (multihop) wireless network. The algorithm is parametrized to allow for tradeoffselectable use as three different variants called RAND, MNF, and PMNF. We provide comprehensive theoretical analysis characterizing the worstcase performance of our algorithm for several classes of problems. In particular, we show that the assignments produced by the PMNF variant are proportional to the thickness of the network. For most typical multihop networks, the thickness can be bounded by a small constant, and hence this represents a significant theoretical result. We also experimentally study the relative performance of the variants for one node and one link assignment problem. We observe that the PMNF variant performs the best, and that a large percentage of unidirectional links is detrimental to the performance in general. 1.
Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots
 Discrete Applied Mathematics
, 2000
"... structure prediction with pseudoknots ..."
A Unified Framework and Algorithm for (T/F/C)DMA Channel Assignment in Wireless Networks
 in IEEE INFOCOM
, 1997
"... Channel assignment problems in the time, frequency and code domains have hitherto been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framew ..."
Abstract

Cited by 38 (0 self)
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Channel assignment problems in the time, frequency and code domains have hitherto been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framework identifies eleven atomic constraints underlying most current and potential assignment problems, and characterizes a problem as a combination of these constraints. Based on this framework, we present a unified algorithm for efficient (T/F/C)DMA channel assignments to network nodes or to internodal links in a (multihop) wireless network. The algorithm is parametrized to allow for use as three different variants  RAND, MNF, and PMNF. We provide comprehensive theoretical analysis characterizing the worstcase performance of our algorithm for several classes of problems. In particular, we show that the assignments produced by the PMNF variant are proportional to the thickness of the network...
On the approximation of protein threading
 Theoretical Computer Science
, 1999
"... In this paper, we study the protein threading problem, which was proposed for predicting a folded 3D protein structure from an amino acid sequence. Since this problem was already proved to be NPhard, we study polynomial time approximation algorithms. We show several hardness results for the approxi ..."
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Cited by 29 (2 self)
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In this paper, we study the protein threading problem, which was proposed for predicting a folded 3D protein structure from an amino acid sequence. Since this problem was already proved to be NPhard, we study polynomial time approximation algorithms. We show several hardness results for the approximation, which includes a MAX SNPhardness result. We also show approximation algorithms for a special case and a general case, where a graph representing interactions between amino acid residues is restricted to be planar in a special case. For this special case, we obtain a constant approximation ratio. @ 1999Elsevier Science B.V. All
ResourceConstrained Geometric Network Optimization (Extended Abstract)
"... We study a variety of geometric network optimization problems on a set of points, in which we are given a resource bound, B, on the total length of the network, and our objective is to maximize the number of points visited (or the total "value" of points visited). In particular, we resol ..."
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Cited by 23 (1 self)
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We study a variety of geometric network optimization problems on a set of points, in which we are given a resource bound, B, on the total length of the network, and our objective is to maximize the number of points visited (or the total "value" of points visited). In particular, we resolve the wellpublicized open problem on the approximability of the rooted "orienteering problem" for the case in which the sites are given as points in the plane and the network required is a cycle. We obtain a 2approximation for this problem. We also obtain approximation algorithms for variants of this problem in which the network required is a tree (3approximation) or a path (2approximation). No prior approximation bounds were known for any of these problems. We also obtain improved approximation algorithms for geometric instances of the unrooted orienteering problem, where we obtain a 2approximation for both the cycle and tree versions of the problem on points in the plane, as well as a ...
An InformationTheoretic Upper Bound on Planar Graphs Using WellOrderly Maps
, 2011
"... This chapter deals with compressed coding of graphs. We focus on planar graphs, a widely studied class of graphs. A planar graph is a graph that admits an embedding in the plane without edge crossings. Planar maps (class of embeddings of a planar graph) are easier to study than planar graphs, but a ..."
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Cited by 23 (4 self)
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This chapter deals with compressed coding of graphs. We focus on planar graphs, a widely studied class of graphs. A planar graph is a graph that admits an embedding in the plane without edge crossings. Planar maps (class of embeddings of a planar graph) are easier to study than planar graphs, but as a planar graph may admit an exponential number of maps, they give little information on graphs. In order to give an informationtheoretic upper bound on planar graphs, we introduce a definition of a quasicanonical embedding for planar graphs: wellorderly maps. This appears to be an useful tool to study and encode planar graphs. We present upper bounds on the number of unlabeled planar graphs and on the number of edges in a random planar graph. We also present an algorithm to compute wellorderly maps and implying an efficient coding of planar graphs.
Drawing Stressed Planar Graphs in Three Dimensions
 In
, 1995
"... There is much current interest among researchers to find algorithms that will draw graphs in three dimensions. It is well known that every 3connected planar graph can be represented as a strictly convex polyhedron. However, no practical algorithms exist to draw a general 3connected planar graph as ..."
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Cited by 18 (0 self)
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There is much current interest among researchers to find algorithms that will draw graphs in three dimensions. It is well known that every 3connected planar graph can be represented as a strictly convex polyhedron. However, no practical algorithms exist to draw a general 3connected planar graph as a convex polyhedron. In this paper we review the concept of a stressed graph and how it relates to convex polyhedra; we present a practical algorithm that uses stressed graphs to draw 3connected planar graphs as strictly convex polyhedra; and show some examples. Key words: graph, stressed graph, convex polyhedron, reciprocal polyhedron 1 Introduction It is well known that 3connected planar graphs can be drawn as convex polyhedra. However, no practical algorithms exist to draw general 3connected planar graphs as convex polyhedra. The twodimensional (2D) drawing in Figure 1 is 3connected and planar, and the corresponding polyhedron is drawn in Figure 2 as three different views. The 2D ...
Constraints in graph drawing algorithms
 Constraints
, 1998
"... Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and g ..."
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Cited by 16 (0 self)
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Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of userdefined constraints. 1.