29498981
Choosability and Edge Choosability of Planar Graphs without Intersecting Triangles
Let G be a planar graph without two triangles sharing a common vertex. We prove that (1) G is 4-choosable and (2) G is edge-$(\Delta(G)+1)$-choosable when its maximum degree $\Delta(G)\ne 5$.
6853966
Total chromatic number of planar graphs with maximum degree ten
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.
26709203
The Linear 2-Arboricity of Outerplanar Graphs
11186519
Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers
Let G be a graph of nonnegative characteristic and let g(G) and @D(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (1) @D(H)= =11; (2) @D(H)= =7; (3) @D(H)= =5 or G does not contain 4-cycles and 5-cycles; (4) @D(H)= =11; (2) col"g(G)= =7; (3) col"g(G)= =5 or G contains no 4-cycles and 5-cycles; (4) col"g(G)=<10 if G does not contain 4-cycles.
1166455
Comparing Graph Representations of Protein Structure for Mining Family-Specific Residue-Based Packing Motifs
We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almost-Delaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almost-Delaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs.
15242556
AFOPT: An Efficient Implementation of Pattern Growth Approach
In this paper, we revisit the frequent itemset mining (FIM) problem and focus on studying the pattern growth approach. Existing pattern growth algorithms differ in several dimensions: (1) item search order; (2) conditional database representation; (3) conditional database construction strategy; and (4) tree traversal strategy. They adopted different strategies on these dimensions. Several adaptive algorithms were proposed to try to find good strategies for general situations. In this paper, we described the implementation techniques of an adaptive pattern growth algorithm, called AFOPT, which demonstrated good performance on all tested datasets. We also extended the algorithm to mine closed and maximal frequent itemsets. Comprehensive experiments were conducted to demonstrate the efficiency of the proposed algorithms.
36275833
Generalized pre-scheduler
A preschedule is a list of "executives" generated offline for a set of time-driven jobs. If in addition there exists event-driven workload competing for resources, sufficient slacks must be embedded in a valid preschedule. A prescheduler was defined in Wang et al. (2003) with the following assumptions: the competing workload is modeled as sporadic tasks and the time-driven jobs to be prescheduled are independent. In this paper, the prescheduling problem is generalized. First, the event-driven workload is no longer limited to sporadic tasks or any specific task model. Instead, a concept called "prescheduling space" is introduced so that the time-driven jobs to be prescheduled are inside the space, the competing event-driven workload is outside the space, and resource competition is abstracted to the space bounded by a supply function and a supply contract. Second, precedence constraints between the time-driven jobs to be prescheduled are allowed. The generalized prescheduler presented in this paper produces a valid preschedule if and only if one exists under the constraints of execution time bounds, valid scopes, precedence requirements and supply contract; otherwise, it returns a notice of failure. The generalized prescheduler runs in time polynomial to the number of time-driven jobs.
6255110
Computing real inflection points of cubic algebraic curves
Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inflection points of a planar cubic algebraic curve f = 0 by directly intersecting f = 0 and its Hessian curve H(f) = 0 requires solving a degree nine univariate polynomial equation, and thus is relatively inefficient. In this paper we present an algorithm for computing the real inflection points of a real planar cubic algebraic curve. The algorithm follows Hilbert's solution for computing the inflection points of a cubic algebraic curve in the complex projective plane. Hilbert's solution is based on invariant theory and requires solving only a quartic polynomial equation and several cubic polynomial equations. Through a detailed study with emphasis on the distinction between real and imaginary inflection points, we adapt Hilbert's solution to efficiently compute only the real inflection points of a cubic algebraic curve f = 0, without exhaustive but unnecessary search and root testing. To compute the real inflection points of f = 0, only two cubic polynomial equations need to be solved in our algorithm and it is unnecessary to solve numerically the quartic equation prescribed in Hilbert's solution. In addition, the invariants of f = 0 are used to analyze the singularity of a singular curve, since the number of the real inflection points of f = 0 depends on its singularity type.
11747548
A multiplex-multicast scheme that improves system capacity of voice-over-IP on wireless LAN by 100%
Voice-over-IP (VoIP) is.an important application on the Internet. With the emergence of WLAN technology and its various advantages compared with the traditional wired LAN, it is fast becoming the "last-mile" of choice for the overall Internet infrastructure. This work considers the support of VoIP over 802.11b WLAN. We show that although the raw WLAN capacity can potentially support more than 500 VoIP sessions, various overheads bring this down to only 12 VoIP sessions when using GSM 6.10 codec. We propose a novel multiplexing scheme for VoIP which exploits multicasting over WLAN for the downlink VoIP traffic. This scheme can achieve nearly 100% improvement in system capacity. In addition, we present results showing that the delay and delay jitter introduced by the proposed scheme are small. We believe that the scheme can reduce the blocking probability of VoIP sessions in an enterprise WLAN significantly.