In this paper, we investigate quantum algorithms for graph colouring problems, in particular for 2- and 3-colouring of graphs. Our main goal is to establish a set of quantum representations and operations suitable for...
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In this paper, we investigate quantum algorithms for graph colouring problems, in particular for 2- and 3-colouring of graphs. Our main goal is to establish a set of quantum representations and operations suitable for the problem at hand. We propose unitaryas well as measurement-based quantum computations, also taking inspiration from answer set programming, a form of declarative programming close to traditional logic programming. The approach used is one in which we first generate arbitrary solutions to the problem, then constraining these according to the problem's input. Though we do not achieve fundamental speed-ups, our algorithms show how quantum concepts can be used for programming and moreover exhibit structural differences. For example, we compute all possible colourings at the same time. We compare our algorithms with classical ones, highlighting how the same type of difficulties give rise to NP-complete behaviour, and propose possible improvements. (C) 2008 Elsevier B.V. All rights reserved.
Simultaneous representations of planar graphs and their duals normally require that the dual vertices to be placed inside their corresponding primal faces, and the edges of the dual graph to cross only their correspon...
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Simultaneous representations of planar graphs and their duals normally require that the dual vertices to be placed inside their corresponding primal faces, and the edges of the dual graph to cross only their corresponding primal edges. Erten and Kobourov [C. Erten, S.G. Kobourov, Simultaneous embedding of a planar graph and its dual on the grid, Theory Computer Systems 38 (2005) 313-327] provided a linear time algorithm on simultaneous straight-line grid embedding of a 3-connected planar graph and its dual such that all the vertices are placed on grid points and each edge is drawn as one straight-line segment except for one which is drawn using two segments. Their drawing size is (2n - 2) x (2n - 2), where n is the total number of vertices in the graph and its dual. They raised an open question on whether there is a large class of planar graphs that allows this simultaneous straight-line grid embedding on a smaller grid. We answer this open question by giving a linear time simultaneous straight-line grid embedding algorithm for a 3-connected planar graph and its dual on a grid of size (n - 1) x n. (c) 2006 Elsevier B.V. All rights reserved.
A path cover of a graph G = (V, E) is a set of pairwise vertex-disjoint paths such that the disjoint union of the vertices of these paths equals the vertex set V of G. The path cover problem is, given a graph, to find...
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A path cover of a graph G = (V, E) is a set of pairwise vertex-disjoint paths such that the disjoint union of the vertices of these paths equals the vertex set V of G. The path cover problem is, given a graph, to find a path cover having the minimum number of paths. The path cover problem contains the Hamiltonian path problem as a special case since finding a path cover, consisting of a single path, corresponds directly to the Hamiltonian path problem. A graph is a distance-hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them. The complexity of the path cover problem on distance-hereditary graphs has remained unknown. In this paper, we propose the first polynomial-time algorithm, which runs in 0(1 V 19) time, to solve the path cover problem on distance-hereditary graphs. (C) 2007 Elsevier B.V. All rights reserved.
Given an edge-weighted graph where all weights are nonnegative reals, an edge reweighting is an assignment of nonnegative reals to edges such that, for each vertex, the sums of given and new weights assigned to the ed...
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Given an edge-weighted graph where all weights are nonnegative reals, an edge reweighting is an assignment of nonnegative reals to edges such that, for each vertex, the sums of given and new weights assigned to the edges incident on the vertex do coincide. An edge is then said to be invariant if its weight is the same for any edge reweighting. We show that the set of invariant edges of an arbitrary edge-weighted graph can be determined in time linear in the size of the underlying graph. Moreover, an application to the security of statistical data is discussed.
Image retrieval from an image database by the image objects and their spatial relationships has emerged as an important research subject in these decades. To retrieve images similar to a given query image, retrieval m...
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Image retrieval from an image database by the image objects and their spatial relationships has emerged as an important research subject in these decades. To retrieve images similar to a given query image, retrieval methods must assess the similarity degree between a database image and the query image by the extracted features with acceptable efficiency and effectiveness. This paper proposes a graph-based model SRG (spatial relation graph) to represent the semantic information of the contained objects and their spatial relationships in an image with no file annotation. In an SRG graph, the image objects are symbolized by the predefined class names as vertices and the spatial relations between object pairs are represented as arcs. The proposed model assesses the similarity degree between two images by calculating the maximum common subgraph of two corresponding SRG's through intersection, which has quadratic time complexity owing to the characteristics of SRG. Its efficiency remains quadratic regardless of the duplication rate of the object symbols. The extended model SRG(T) is also proposed, with the same time complexity, for the applications that need to consider the topological relations among objects. A synthetic symbolic image database and an existing image dataset are used in the conducted experiments to verify the performance of the proposed models. The experimental results show that the proposed models have compatible retrieval quality with remarkable efficiency improvements compared with three well-known methods LCS_Clique, SIMR, and 2D Be-string, where LCS_Clique utilizes the number of objects in the maximum common sub-image as its similarity function, SIMR uses accumulation-based similarity function of similar object pairs, and 2D Be-string calculates the similarity of 2D patterns by the linear combination of two 1D similarities. (C) 2007 Elsevier B.V. All rights reserved.
This paper deals with the characterization and the recognition of graph classes. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately, this strategy rarely...
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This paper deals with the characterization and the recognition of graph classes. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately, this strategy rarely leads to a very efficient recognition algorithm. On the other hand, many graph classes can be efficiently recognized by techniques that use some ordering of the nodes, such as the one given by a traversal. We specifically study graphs that have an ordering avoiding some ordered structures. More precisely, we consider structures that we call patterns on three nodes, and we study the complexity of recognizing the classes associated with such patterns. In this domain, there are three key previous works. Independently Skrien [J. graph Theory, 6 (1982), pp. 309-316] and Damashke [Forbidden ordered subgraphs, in Topics in Combinatorics and graph Theory, Physica-Verlag HD, 1990, pp. 219-229] noted that several graph classes, such as chordal, bipartite, interval, and comparability graphs, have a characterization in terms of forbidden patterns. On the algorithmic side, Hell, Mohar, and Rafiey [Ordering without forbidden patterns, in algorithms-ESA 2014, Springer, 2014, pp. 554-565] proved that any class defined by a set of forbidden patterns on three nodes can be recognized in time O(n(3)) by using an algorithm based on an extension of 2-SAT. We improve on these two lines of works by systematically characterizing all the classes defined by sets of forbidden patterns (on three nodes) and proving that among the 22 different classes (up to complement) that we find, 20 can actually be recognized in linear time. Beyond these results, we consider that this type of characterization is very useful from an algorithmic perspective, leads to a rich structure of classes, and generates many algorithmic and structural open questions worth investigating.
Ontologies are domain-specific metadata that describe relationships between a specific field's properties, sample data of this field, and properties developed for many different purposes. Also, ontologies can be d...
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Ontologies are domain-specific metadata that describe relationships between a specific field's properties, sample data of this field, and properties developed for many different purposes. Also, ontologies can be defined by other names within the same domain. Ontology matching algorithms eliminate definition differences and find similarities between existing ontologies. Ontology matching algorithms are used especially for information management, data integration, information extraction, etc. In this study, a graph-based framework is proposed to match large ontologies. This framework is aimed to divide the large ontologies into small pieces and then matches them using sub-graph mining algorithms. Karger algorithm and CP (clique percolation and nearest neighbor) algorithm are used to divide large ontologies. Both algorithms were applied to ontologies for the first time. In the next step, these obtained sub-parts are matched by using sub-graph mining algorithms. GraMi and gSpan algorithms were selected and were used for the first time in the field of ontology matching. We validated our framework using Anatomy and Conference data sets. Also, the proposed framework is compared with widely used in the literature AML and Falcon-AO matching algorithms. According to obtained the results, it is seen that GraMi is better than matching algorithms.
In this paper we consider graph traversal problems (Euler and Travelling Salesman traversals) that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). We first explain the connec...
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In this paper we consider graph traversal problems (Euler and Travelling Salesman traversals) that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). We first explain the connection of the graph problems to SBH and then focus on the traversal problems. We describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide bounded-error approximation algorithms for the maximum weight TSP in a superset of those directed graphs. We also establish the existence of a matroid structure defined on the set of Euler and Hamilton paths in the restricted class of graphs. 1998 Published by Elsevier Science B.V. All rights reserved.
Recently, several studies have reported that graph Convolutional Networks (GCN) exhibit defects in integrating node features and topological structures in graphs. Although the proposal of AMGCN compensates for the dra...
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Recently, several studies have reported that graph Convolutional Networks (GCN) exhibit defects in integrating node features and topological structures in graphs. Although the proposal of AMGCN compensates for the drawbacks of GCN to some extent, it still cannot solve GCN's insufficient fusion abilities fundamentally. Thus it is essential to find a network component with stronger fusion abilities to substitute GCN. Meanwhile, a Deep Adaptive graph Neural Network (DAGNN) proposed by Liu et al. can adaptively aggregate information from different hops of neighborhoods, which remarkably benefits its fusion abilities. To replace GCN with DAGNN network in AMGCN model and further strengthen the fusion abilities of DAGNN network itself, we make further improvements based on DAGNN model to obtain DAGNN variant. Moreover, experimentally the fusion abilities of the DAGNN variant are verified to be far stronger than GCN. And then build on that, we propose a Deep Adaptive Multi-channel graph Neural Network (DAMGNN). The results of lots of comparative experiments on multiple benchmark datasets show that the DAMGNN model can extract relevant information from node features and topological structures to the maximum extent for fusion, thus significantly improving the accuracy of node classification.
In this paper we study the problem of protecting sensitive data in an n by n two-dimensional table of statistics, when the nonsensitive data are made public along with the row and column sums for the table. A sensitiv...
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In this paper we study the problem of protecting sensitive data in an n by n two-dimensional table of statistics, when the nonsensitive data are made public along with the row and column sums for the table. A sensitive cell is considered unprotected if its exact value can be deduced from the nonsensitive cell values and the row and column sums. We give an efficient algorithm to identify all unprotected cells in a table. The algorithm runs in linear time if the sensitive values are known, and in O(n
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