14716028
New Upper Bounds for Ramsey Numbers
The Ramsey numberR(G1,G2) is the smallest integerpsuch that for any graphGonpvertices eitherGcontainsG1orGcontainsG2, whereGdenotes the complement ofG. LetR(m,n)=R(Km,Kn). Some new upper bound formulas are obtained forR(G1,G2andR(m,n), and we derive some new upper bounds for Ramsey numbers here.
29686713
A note on Ramsey numbers with two parameters
The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or G- contains G2, where G- denotes the complement of G. In this paper, some new bounds with two parameters for the Ramsey number R(G1, G2), under some assumptions, are obtained. Especially, we prove that R(K6 - e, K6) ≤ 116 and R(K6 - e, K7) ≤ 202, these improve the two upper bounds for the classical Ramsey number in [S.P. Radziszowski, Small Ramsey number, Electron. J. Combin. DSI (2002) 1-36].
41406916
A bound for multicolor Ramsey numbers
Abstract The Ramsey number R(G 1 , G 2 , …, G n ) is the smallest integer p such that for any n -edge coloring (E 1 ,E 2 , …, E n ) of K p , K p [E i ] contains G i for some i , G i as a subgraph in K p [E i ] . Let R(m 1 ,m 2 , …, m n )≔R(K m 1 ,K m 2 , …, K m n ),R(m;n)≔R(m 1 ,m 2 ,…,m n ) if m i =m for i=1, 2,…,n . A formula is obtained for R(G 1 ,G 2 , …, G n ) .
45980557
A new idea for Hamiltonian problem
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.
27951187
The Ramsey numbers of trees versus W6 or W7
Let Tn denote a tree of order n and Wm a wheel of order m + 1. In this paper, we show the Ramsey numbers R(Tn, W6) = 2n - 1 + µ for n ≥ 5, where µ = 2 if Tn = Sn, µ = 1 if Tn = Sn(1, 1) or Tn = Sn(1, 2) and n ≡ 0 (mod 3), and µ = 0 otherwise; R(Tn, W7) = 3n - 2 for n ≥ 6.
7869643
Fast parallel algorithms for the unit cost editing distance between trees
We present three algorithms to find the distance. The first algorithm is a simple dynamic programming algorithm based on a postorder traversal whose complexity improves upon the best previously published algorithm due to Tai (T79 in JACM). The second and third algorithms are parallel algorithms based on the application of suffix trees to the comparison problem. The cost of executing these algorithms is a monotonic increasing function of the distance between the two trees. Results Let trees T I and T2 have numbers of levels L i and L 2 respectively. Let k be the actual distance between T 1 and T2. Let N be rain (IT11, IT2 ]). The asymptotic running times (assuming a concurrentread concurrent-write parallel random access machine) are:
9738891
Comparing multiple RNA secondary structures using tree comparisons
In a previous paper, an algorithm was presented for analyzing multiple RNA secondary structures utilizing a multiple string alignment algorithm. In this paper we present another approach to the problem of comparing many secondary structures by utilizing a very efficient tree-matching algorithm that will compare two trees in O([T1] X [T2] X L1 X L2) in the worst case and very close to O([T1] X [T2]) for average trees representing secondary structures. The result of the pairwise comparison algorithm is then used with a cluster algorithm to produce a multiple structure clustering which can be displayed in a taxonomy tree to show related structures.
5200887
Damage pattern mining in hurricane image databases
We present a damage pattern mining framework for hurricane data on residential houses using aerial photographs with 1:3000 based scale. The vertical photographs are normally collected for an overview of a disaster area or for more detailed assessment. Damage on roof, especially for shingles torn off, is expected to be discovered in a more efficient and automatic way instead of going through the high-resolution aerial photograph for numerous details. The discovered damage patterns can then be used for hurricane damage assessment and impacts on different geographical areas. Our methodology is: (1) applying a novel and effective segmentation method on each residential house on the aerial photograph of one community, (2) using the segmentation results to obtain a set of indexing parameters for each house representing the damage level of roof cladding as well as the patterns of damage, (3) using these parameters to select several templates representing the damage patterns so that users can issue query-by-example (QBE) queries. The proposed segmentation method is an unsupervised simultaneous partition and class parameter estimation algorithm that considers the problem of segmentation as a joint estimation of the partition and class parameter variables. By utilizing this segmentation method, the indexing parameters can be obtained automatically. The QBE capability can assist in finding similar damage patterns on the roof of the residential houses in different locations in the image databases. Experiments based on the aerial photographs of Hurricane Andrew in 1992 are conducted and analyzed to show the effectiveness of the proposed hurricane damage pattern mining framework.
29387350
Efficient and robust feature extraction by maximum margin criterion
In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal component analysis (PCA) and linear discriminant analysis (LDA) are the two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features, and LDA is not stable due to the small sample size problem . In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.
16504753
Minimizing downtime in seamless migrations of mobile applications
Application migration is a key enabling technology component of mobile computing that allows rich semantics involving location awareness, trust and timeliness of information processing by moving the application where the data is. Seamlessness is one of the key properties of mobile computing and downtime must be eliminated/minimized during the migration to achieve seamlessness. But migration involves large overheads, dominant of which are the overheads due to serialization and de-serialization [1]. To achieve seamless migration, an application state could be pre-serialized during the program's execution, and upon migration, the serialized data could be transmitted and de-serialized to get the execution started. Previous approach to this problem [1] removed dead state but still suffered from large migration overheads due to serialization on-demand that could lead to an unacceptable downtime.In this work, we develop a static compiler analysis plus runtime assisted framework to decrease the migration overhead to almost zero while minimizing the degradation in the program's performance. We achieve such a goal by deciding which data to be pre-serialized through analysis, and pre-serializing the state in the program. A safe state is kept that would allow immediate migration upon the arrival of an interrupt while minimizing frequent pre-serialization. When the migration interrupt comes in, the serialized data can be transmitted directly to the destination machine. This allows an application to resume its execution at the destination machine with almost no interruption (only a small amount of non-serialized data needs to be serialized during migration). The optimization serializes the data in such a way that a maximal number of functions can execute without interruption after migration. Our experiments with multimedia applications show that the migration latency is significantly reduced leading to a small downtime. Thus, the contribution of the paper is to provide an efficient methodology to perform seamless migration while limiting the overhead.