6176366
The Ramsey numbers of stars versus wheels
For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest positive integer n such that for any graph G of order n, either G contains G 1 or the complement of G contains G 2 . Let S n denote a star of order n and W m a wheel of order m + 1. This paper shows that R(S n , W 6 )=2n + 1 for n ≥ 3 and R(S n , W m )=3n - 2 for m odd and n ≥ m - 1 ≥ 2.
4357183
A New Proof of Wojcicka's Conjecture
A graph G is 3-domination-critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Wojcicka conjectured that every 3-domination-critical graph with δ ≥ 2 has a hamiltonian cycle (J. Graph Theory 14 (1990) 205-215). The conjecture had been proved and its proof consists of two parts: the case α ≤ δ + 1 (J. Graph Theory 25 (1997) 173-184) and the case α = δ + 2 (Discrete Appl. Math. 92 (1999) 57-70). In this paper, we give a new and simple proof of the conjecture by using Hanson's (J. Combin. Math. Combin. Comput. 13 (1993) 121-128) and Bondy-Chvatal's (Discrete Math. 15(1976) 111-135) closure operations.
2252308
Cost-Driven Hybrid Configuration Prefetching for Partial Reconfigurable Coprocessor
Reconfigurable computing systems have developed the capability of changing the configuration of the reconfigurable coprocessor multiple times during the course of a program. However, in most systems the reconfigurable coprocessor wastes computation cycles while waiting for the reconfiguration to complete. Therefore, the high demand for frequent run-time reconfiguration directly translates into higher reconfiguration overhead. Some studies have introduced the concept of prefetching to reduce the reconfiguration overhead. However, these prefetching algorithms are probability-driven. We believe that including configuration size information in the prediction algorithm directly links the training of the predictor with the performance gain. Therefore we proposed a performance-oriented cost-driven algorithm for coarse-grained configuration prefetching. Our cycle accurate simulation results show that the proposed cost-driven algorithm outperforms the probability-driven predictor by 10.8% to 29.6% in reducing reconfiguration overhead.
16940810
Vertex and Tree Arboricities of Graphs
This paper studies the following variations of arboricity of graphs. The vertex (respectively, tree) arboricity of a graph G is the minimum number va(G) (respectively, ta(G)) of subsets into which the vertices of G can be partitioned so that each subset induces a forest (respectively, tree). This paper studies the vertex and the tree arboricities on various classes of graphs for exact values, algorithms, bounds, hamiltonicity and NP-completeness. The graphs investigated in this paper include block-cactus graphs, series-parallel graphs, cographs and planar graphs.
16583184
Using cluster skeleton as prototype for data labeling
A new approach, designed for clustering data whose underlying distribution shapes are arbitrary, is presented. This study is concerned with the use of the skeleton of a cluster as its prototype, which can represent the cluster more closely than that of using a single data point. The given data set is then partitioned into those skeleton-represented clusters without any prior knowledge nor assumptions of hidden structures. A novel function called cluster characteristic function (CCF) has been constructed and the associated theorems have been proposed and proved that the proper number of clusters can be determined with the approach.
33065239
Triangle-free Hamiltonian Kneser graphs
The Kneser graph K(n,k) has as vertices the k-subsets of {1, 2,...,n}. Two vertices are adjacent if the k-sets are disjoint. When n > 3k, the Kneser Graph K(n, k) has no triangle. In this paper, we prove that K(n,k) is Hamiltonian for n ≥ (3k + 1 + √5k2- 2k + 1)/2, and extend this to the bipartite Kneser graphs. Note that (3k + 1 + √5k2 - 2k + 1)/2 > 2.62k + 1.
21454000
Modelling software operational reliability via input domain-based reliability growth model
Operational reliability of programs depends upon many factors imposed by design, testing, and operation of the programs. In the testing stage, the main imperfect factors which can affect operational reliability are faults, testing time, fault correction, testing profile and operation profile. The proposed modelling process takes these factors into account. It consists of two testing stages and one operational stage. In the testing stages, partition testing and an input domain-based reliability growth model are used to evaluate the reliability growth. Based on the profile coverage between testing and operational profiles, a method is developed to partition the input domain, so that the testing profile can follow the given operational profile of a program. In the operational stage, the proposed reliability model uses the remaining faults from testing stages as the source of unreliability. A case study is conducted using the proposed models.