Results 1  10
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28
Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related ..."
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Cited by 47 (6 self)
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The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science
The bidimensionality Theory and Its Algorithmic Applications
 Computer Journal
, 2005
"... This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixedparameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, boundedgenus graphs and gra ..."
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Cited by 27 (1 self)
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This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixedparameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, boundedgenus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the Graph Minor Theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. Here, we summarize the known combinatorial and algorithmic results of bidimensionality theory with the highlevel ideas involved in their proof; we describe the previous work on which the theory is based and/or extends; and we mention several remaining open problems. 1.
Recognizing string graphs in NP
 J. of Computer and System Sciences
"... A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable u ..."
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Cited by 24 (4 self)
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A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable until very recently, when two independent papers established exponential upper bounds on the number of intersections needed to realize a string graph (Pach and Tóth, 2001; Schaefer and ˇ Stefankovič, 2001). These results implied that the recognition problem lies in NEXP. In the present paper we improve this by showing that the recognition problem for string graphs is in NP, and therefore NPcomplete, since Kratochvíl showed that the recognition problem is NPhard (Kratochvíl, 1991b). The result has consequences for the computational complexity of problems in graph drawing, and topological inference. We also show that the string graph problem is decidable for surfaces of arbitrary genus. Key words: String graphs, NPcompleteness, graph drawing, topological inference, Euler diagrams
Combining Topological and Size Information for Spatial Reasoning
 Artificial Intelligence
, 2000
"... Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Regi ..."
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Cited by 17 (7 self)
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Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but three large maximal tractable subclasses of RCC8, called b H8 , C8 and Q8 respectively, have been identied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 relations and qualitative size relations forming a Point Algebra, where n is the number of spatial regions. This algorithm is correct and complete for deciding consistency when the topological relations are either in b H8 , C8 or Q8 , and has the same complexity as the best known method for deciding consistency...
Fast algorithms for hard graph problems: Bidimensionality, minors, and local treewidth
 In Proceedings of the 12th International Symposium on Graph Drawing, volume 3383 of Lecture Notes in Computer Science
, 2004
"... Abstract. This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems. 1 ..."
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Cited by 10 (3 self)
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Abstract. This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems. 1
Algorithmic graph minor theory: Improved grid minor bounds and wagner’s contraction
 Proceedings of the Third International Conference on Distributed Computing and Internet Technology
, 2006
"... ..."
Parallel Algorithms for Hamiltonian Problems on Quasithreshold Graphs
 Parallel and Distributed Computing
, 1998
"... In this paper we show structural and algorithmic properties on the class of quasithreshold graphs, or QTgraphs for short, and prove necessary and sufficient conditions for a QTgraph to be Hamiltonian. Based on these properties and conditions, we construct an efficient parallel algorithm for findi ..."
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Cited by 6 (6 self)
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In this paper we show structural and algorithmic properties on the class of quasithreshold graphs, or QTgraphs for short, and prove necessary and sufficient conditions for a QTgraph to be Hamiltonian. Based on these properties and conditions, we construct an efficient parallel algorithm for finding a Hamiltonian cycle in a QTgraph; for an input graph on n vertices and m edges, our algorithm takes O(log n) time and requires O(n + m) processors on the CREW PRAM model. In addition, we show that the problem of recognizing whether a QTgraph is a Hamiltonian graph and the problem of computing the Hamiltonian completion number of a non Hamiltonian QTgraph can also be solved in O(log n) time with O(n + m) processors. Our algorithms rely on O(log n)time parallel algorithms, which we develop here, for constructing tree representations of a QTgraph; we show that a QTgraph G has a unique tree representation, that is, a tree structure which meets the structural properties of G. We also present parallel algorithms for other optimization problems on QTgraphs which run in O(log n) time using a linear number of processors.
The number of spanning trees in Kncomplements of quasithreshold graphs
, 2005
"... In this paper we examine the classes of graphs whose Kncomplements are trees and quasithreshold graphs and derive formulas for their number of spanning trees; for a subgraph H of Kn, the Kncomplement of H is the graph Kn âH which is obtained from Kn by removing the edges of H. Our proofs are b ..."
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Cited by 5 (2 self)
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In this paper we examine the classes of graphs whose Kncomplements are trees and quasithreshold graphs and derive formulas for their number of spanning trees; for a subgraph H of Kn, the Kncomplement of H is the graph Kn âH which is obtained from Kn by removing the edges of H. Our proofs are based on the complement spanningtree matrix theorem, which expresses the number of spanning trees of a graph as a function of the determinant of a matrix that can be easily constructed from the adjacency relation of the graph. Our results generalize previous results and extend the family of graphs of the form Kn â H admitting formulas for the number of their spanning trees.
S.: Laplacian spectrum of weakly quasithreshold graphs
 Graphs Combin
, 2008
"... Abstract. In this paper we study the class of weakly quasithreshold graphs that are obtained from a vertex by recursively applying the operations (i) adding a new isolated vertex, (ii) adding a new vertex and making it adjacent to all old vertices, (iii) disjoint union of two old graphs, and (iv) a ..."
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Cited by 4 (0 self)
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Abstract. In this paper we study the class of weakly quasithreshold graphs that are obtained from a vertex by recursively applying the operations (i) adding a new isolated vertex, (ii) adding a new vertex and making it adjacent to all old vertices, (iii) disjoint union of two old graphs, and (iv) adding a new vertex and making it adjacent to all neighbours of an old vertex. This class contains the class of quasithreshold graphs. We show that weakly quasithreshold graphs are precisely the comparability graphs of a forest consisting of rooted trees with each vertex of a tree being replaced by an independent set. We also supply a quadratic time algorithm in the the size of the vertex set for recognizing such a graph. We completely determine the Laplacian spectrum of weakly quasithreshold graphs. It turns out that weakly quasithreshold graphs are Laplacian integral. As a corollary we obtain a closed formula for the number of spanning trees in such graphs. A conjecture of Grone and Merris asserts that the spectrum of the Laplacian of any graph is majorized by the conjugate of the degree sequence of the graph. We show that the conjecture holds for cographs.
Recognizing holefree 4map graphs in cubic time
 Algorithmica
"... We present a cubictime algorithm for the following problem: Given a simple graph, decide whether it is realized by adjacencies of countries in a map without holes, in which at most four countries meet at any point. ..."
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Cited by 4 (0 self)
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We present a cubictime algorithm for the following problem: Given a simple graph, decide whether it is realized by adjacencies of countries in a map without holes, in which at most four countries meet at any point.