Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

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Graph Coloring Problems

Discovery of association rules is an important problem in database mining. In this paper we present new algorithms for fast association mining, which scan the database only once, addressing the open question whether all the rules can be efficiently extracted in a single database pass. The algorithms use novel itemset clustering techniques to approximate the set of potentially maximal frequent itemsets. The algorithms then make use of efficient lattice traversal techniques to generate the frequent itemsets contained in each cluster. We propose two clustering schemes based on equivalence classes and maximal hypergraph cliques, and study two traversal techniques based on bottom-up and hybrid search. We also use a vertical database layout to cluster related transactions together. Experimental results show improvements of over an order of magnitude compared to previous algorithms.

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New algorithms for fast discovery of association rules

The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].

The maximum clique problem

This paper describes a general technique that can be used to obtain approximation schemes for various NP-complete problems on planar graphs. The strategy depends on decompos- ing a planar graph into subgraphs of a form we call k-outerplanar. For fixed k, the problems of interest are solvable optimally in linear time on k-outerplanar graphs by dynamic programming. For general planar graphs, if the problem is a maximization problem, such as maximum independent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least k/(k + 1)optimal. If the problem is a minimization problem, such as minimum vertex cover, it gives for each k a linear time algorithm that produces a solution whose size is at most (k + 1)/k optimal. Taking k = (c log log nl or k = (c log nl, where n is the number of nodes and c is some constant, we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases. The class of problems for which this approach provides approximation schemes includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominat- ing set, and minimum edge dominating set. For these and certain other problems, the proof of solvability on k-outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time.

Approximation algorithms for NP-complete problems on planar graphs

Complexity and Approximation

We propose a fast, high quality tone mapping technique to display high contrast images on devices with limited dynamic range of luminance values. The method is based on logarithmic compression of luminance values, imitating the human response to light. A bias power function is introduced to adaptively vary logarithmic bases, resulting in good preservation of details and contrast. To improve contrast in dark areas, changes to the gamma correction procedure are proposed. Our adaptive logarithmic mapping technique is capable of producing perceptually tuned images with high dynamic content and works at interactive speed. We demonstrate a successful application of our tone mapping technique with a high dynamic range video player enabling to adjust optimal viewing conditions for any kind of display while taking into account user preference concerning brightness, contrast compression, and detail reproduction.

/pdf/adaptive-logarithmic-mapping-for-displaying-high-contrast-1bph2oxtis.pdf

Adaptive Logarithmic Mapping For Displaying High Contrast Scenes

In this paper we introduce a new simple strategy into edge-searching of a graph, which is useful to the various subgraph listing problems. Applying the strategy, we obtain the following four algorithms. The first one lists all the triangles in a graph G in $O(a(G)m)$ time, where m is the number of edges of G and $a(G)$ the arboricity of G. The second finds all the quadrangles in $O(a(G)m)$ time. Since $a(G)$ is at most three for a planar graph G, both run in linear time for a planar graph. The third lists all the complete subgraphs $K_l $ of order l in $O(la(G)^{l - 2} m)$ time. The fourth lists all the cliques in $O(a(G)m)$ time per clique. All the algorithms require linear space. We also establish an upper bound on $a(G)$ for a graph $G:a(G) \leqq \lceil (2m + n)^{1/2} \rceil $, where n is the number of vertices in G.

Arboricity and subgraph listing algorithms

A linear algorithm for embedding planar graphs using PQ -trees

http://www.ecei.tohoku.ac.jp/alg/nishizeki/sub/j/DVD/PDF_J/J075.pdf

The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs

This paper presents two efficient algorithms for drawing plane graphs nicely. Both draw all edges of a graph as straight line segments without crossing lines. The first draws a plane graph “convex” if possible, that is, in a way that every inner face and the complement of the outer face are convex polygons. The second, using the first, produces a pleasing drawing of a given plane graph that satisfies the following property as far as possible: the complements of 3-connected components, together with inner faces and the complement of the outer face, are convex polygons. The running time and storage space of both algorithms are linear in the number of vertices of the graph.

/pdf/drawing-plane-graphs-nicely-512jckydif.pdf

Norishige Chiba

Papers

Adaptive Logarithmic Mapping For Displaying High Contrast Scenes

Arboricity and subgraph listing algorithms

A linear algorithm for embedding planar graphs using PQ -trees

The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs

Drawing plane graphs nicely