18746420
Bordeaux 3-color conjecture and 3-choosability
A graph G=(V,E) is list L-colorable if for a given list assignment L={L(v):v@?V}, there exists a proper coloring c of G such that c(v)@?L(v) for all v@?V. If G is list L-colorable for every list assignment with |L(v)|>=k for all v@?V, then G is said to be k-choosable. In this paper, we prove that (1) every planar graph either without 4- and 5-cycles, and without triangles at distance less than 4, or without 4-, 5- and 6-cycles, and without triangles at distance less than 3 is 3-choosable; (2) there exists a non-3-choosable planar graph without 4-cycles, 5-cycles, and intersecting triangles. These results have some consequences on the Bordeaux 3-color conjecture by Borodin and Raspaud [A sufficient condition for planar graphs to be 3-colorable. J. Combin. Theory Ser. B 88 (2003) 17-27].
6853966
Total chromatic number of planar graphs with maximum degree ten
41218825
Relaxed game chromatic number of graphs
This paper discusses a coloring game on graphs. Let k, d be non-negative integers and C a set of k colors. Two persons, Alice and Bob, alternately color the vertices of G with colors from C, with Alice having the first move. A color i is legal for an uncolored vertex x if by coloring x with color i, the subgraph of G induced by those vertices of color i has maximum degree at most d. Each move of Alice or Bob colors an uncolored vertex with a legal color. The game is over if either all vertices are colored, or no more vertices can be colored with a legal color. Alice's goal is to produce a legal coloring which colors all the vertices of G, and Bob's goal is to prevent this from happening. We shall prove that if G is a forest, then for k = 3, d ≥ 1, Alice has a winning strategy. If G is an outerplanar graph, then for k = 6 and d ≥ 1, Alice has a winning strategy.
13354529
Edge-pancyclicity of coupled graphs
The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.
1003852
Upper Bounds of Entire Chromatic Number of Plane Graphs
The entire chromatic number χvef (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. Kronk and Mitchem (1973) conjectured that χvef (G) ≤ 1 + 4 for every plane graph G. In this paper we prove the conjecture for a plane graph G having χ ′(G) = 1 and give a upper bound χvef (G) ≤ 1+ 5 for all plane graphs, where χ ′(G) and 1 are the chromatic index and the maximum degree of G, respectively.
9810371
The edge-face choosability of plane graphs
A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)|=k for every edge and face x, there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree Δ(G) is (Δ(G)+3)-edge-face choosable.
3122822
Clustering pair-wise dissimilarity data into partially ordered sets
Ontologies represent data relationships as hierarchies of possibly overlapping classes. Ontologies are closely related to clustering hierarchies, and in this article we explore this relationship in depth. In particular, we examine the space of ontologies that can be generated by pairwise dissimilarity matrices. We demonstrate that classical clustering algorithms, which take dissimilarity matrices as inputs, do not incorporate all available information. In fact, only special types of dissimilarity matrices can be exactly preserved by previous clustering methods. We model ontologies as a partially ordered set (poset) over the subset relation. In this paper, we propose a new clustering algorithm, that generates a partially ordered set of clusters from a dissimilarity matrix.
1103015
Visualization of wormholes in sensor networks
Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDS-VOW, to detect wormholes in a sensor network. MDS-VOW first reconstructs the layout of the sensors using multi-dimensional scaling. To compensate the distortions caused by distance measurement errors, a surface smoothing scheme is adopted. MDS-VOW then detects the wormhole by visualizing the anomalies introduced by the attack. The anomalies, which are caused by the fake connections through the wormhole, bend the reconstructed surface to pull the sensors that are faraway to each other. Through detecting the bending feature, the wormhole is located and the fake connections are identified. The contributions of MDS-VOW are: (1) it does not require the sensors to be equipped with special hardware, (2) it adopts and combines the techniques from social science, computer graphics, and scientific visualization to attack the problem in network security. We examine the accuracy of the proposed mechanism when the sensors are deployed in a circle area and one wormhole exists in the network. The results show that MDS-VOW has a low false alarm ratio when the distance measurement errors are not large.
8630623
Gene ontology friendly biclustering of expression profiles
The soundness of clustering in the analysis of gene expression profiles and gene function prediction is based on the hypothesis that genes with similar expression profiles may imply strong correlations with their functions in the biological activities. Gene ontology (GO) has become a well accepted standard in organizing gene function categories. Different gene function categories in GO can have very sophisticated relationships, such as 'part of' and 'overlapping'. Until now, no clustering algorithm can generate gene clusters within which the relationships can naturally reflect those of gene function categories in the GO hierarchy. The failure in resembling the relationships may reduce the confidence of clustering in gene function prediction. In this paper, we present a new clustering technique, smart hierarchical tendency preserving clustering (SMTP-clustering), based on a bicluster model, tendency preserving cluster (TP-Cluster). By directly incorporating gene ontology information into the clustering process, the SMTP-clustering algorithm yields a TP-cluster tree within which any subtree can be well mapped to a part of the GO hierarchy. Our experiments on yeast cell cycle data demonstrate that this method is efficient and effective in generating the biological relevant TP-clusters.
9657581
k-anycast game in selfish networks
Conventionally, the majority of network routing protocols assume that every network terminal or link forwards data for others without any deviation. However, this may not be true when the terminals or links are owned by individual selfish users, who always tries to maximize their own benefits instead of faithfully following a prescribed protocol. In this paper, we propose a new routing protocol, called k-anycast routing, that works well even if network links (or terminals or both) are selfish. In our protocol, the source node first finds a tree that spans k receivers out of a set of possible receivers and pay the relay links to compensate their costs. We prove that every relay link follows the routing protocol: it maximizes its profit when it declares its actual cost
16374313
A self-tuning page cleaner for DB2
The buffer pool in a DBMS is used to cache the disk pages of the database. Because typical database workloads are I/O-bound, the effectiveness of the buffer pool management algorithm is a crucial factor in the performance of the DBMS. In IBM's DB2 buffer pool, the page cleaning algorithm is used to write changed pages to disks before they are selected for replacement. We conducted a detailed study of page cleaning in DB2 version 7.1.0 for Windows by both trace-driven simulation and measurements. Our results show that system throughput can be increased by 19% when the page cleaning algorithm is carefully tuned. In practice, however the manual tuning of this algorithm is difficult. A self-tuning algorithm for page cleaning is proposed posed in this paper to automate this tuning task. Simulation results show that the self-tuning algorithm can achieve performance comparable to the best manually tuned system.