On K1, k-factorizations of a complete bipartite graph
We present a necessary condition for a complete bipartite graph K m,n to be K 1, k -factorizable and a sufficient condition for K m,n to have a K 1, k -factorization whenever k is a prime number. These two conditions provide Ushio's necessary and sufficient condition for K m,n to have a K 1,2 -factorization.

title: On Covering a Bipartite Graph with Cycles
abstract: We conjectured in [H. Wang,  (1999), pp. 115--121] that, for each integer $k\geq 2$, there exists N(k) such that if G=(V1,V2;E) is a bipartite graph with $|V_1|=|V_2|=n\geq N(k)$ and d(x)+d(y)\geq n+k$ for each pair of nonadjacent vertices x and y of G with $x\in V_1$ and $y\in V_2$, then for any k independent edges e1, . . ., ek of G, there exist k vertex-disjoint cycles C1, . . . ,Ck in G such that $e_i\in E(C_i)$ for all $i\in\{1,\ldots ,k\}$ and $V(C_1\cup\cdots \cup C_k)=V(G)$. This conjecture is also verified for k=2 in [H. Wang,  (1999), pp. 115--121]. We prove this conjecture for k=3 in this paper.

title: On Independent Cycles in a Bipartite Graph
abstract: Let G=(V1,V2;E) be a bipartite graph with 2k≤m=|V1|≤|V2|=n, where k is a positive integer. We show that if the number of edges of G is at least (2k−1)(n−1)+m, then G contains k vertex-disjoint cycles, unless e(G)=(2k−1)(n−1)+m and G belongs to a known class of graphs.

title: Packing Three Copies of a Tree into a Complete Graph
abstract: A three T of order n is said to be 3-placeable if there are three edge-disjoint copies of T in Kn. In this paper we characterize all the trees T such that T is 3-placeable.

title: Vertex-Disjoint Triangles in Claw-Free Graphs with Minimum Degree at Least Three
abstract: . Our main result is as follows: For any integer , if G is a claw-free graph of order at least and with minimum degree at least 3, then G contains k vertex-disjoint triangles unless G is of order and G belongs to a known class of graphs. We also construct a claw-free graph with minimum degree 3 on n vertices for each such that it does not contain k vertex-disjoint triangles. We put forward a conjecture on vertex-disjoint triangles in -free graphs.

title: On Quadrilaterals and Cycle Covers in a Bipartite Graph

title: A Polygon Detection Algorithm for Robot Visual Servoing
abstract: The problem of detecting polygon structures in images arises in many applications, from building extraction to cryo-electron microscopy. In this paper, A polygon detection algorithm (PDA) based on line detection is proposed. First of all, we introduce a parallel thinning algorithm to eliminate useless feature points. Then the feature points are organized as disjoint feature contours. For each independent contour, we detect line segment candidates based on RANSAC algorithm. With these candidates, a polygon (triangle, rectangle or other polygons) is composed. Compared to the state-of-the-art shape detection algorithms, PDA is much faster and it can detect any polygons such as triangles, rectangles, etc. We introduce PDA to a 6DOFs robot visual servoing platform and the experimental results show that significant improvements in time efficiency and performance robustness of the proposed algorithm have been achieved.

title: Merge: a programming model for heterogeneous multi-core systems
abstract: In this paper we propose the Merge framework, a general purpose programming model for heterogeneous multi-core systems. The Merge framework replaces current ad hoc approaches to parallel programming on heterogeneous platforms with a rigorous, library-based methodology that can automatically distribute computation across heterogeneous cores to achieve increased energy and performance efficiency. The Merge framework provides (1) a predicate dispatch-based library system for managing and invoking function variants for multiple architectures; (2) a high-level, library-oriented parallel language based on map-reduce; and (3) a compiler and runtime which implement the map-reduce language pattern by dynamically selecting the best available function implementations for a given input and machine configuration. Using a generic sequencer architecture interface for heterogeneous accelerators, the Merge framework can integrate function variants for specialized accelerators, offering the potential for to-the-metal performance for a wide range of heterogeneous architectures, all transparent to the user. The Merge framework has been prototyped on a heterogeneous platform consisting of an Intel Core 2 Duo CPU and an 8-core 32-thread Intel Graphics and Media Accelerator X3000, and a homogeneous 32-way Unisys SMP system with Intel Xeon processors. We implemented a set of benchmarks using the Merge framework and enhanced the library with X3000 specific implementations, achieving speedups of 3.6x -- 8.5x using the X3000 and 5.2x -- 22x using the 32-way system relative to the straight C reference implementation on a single IA32 core.

title: A New Graph Approach to Minimizing Processor Fragmentation in Hypercube Multiprocessors
abstract: The authors propose a new approach for subcube and noncubic processor allocations for hypercube multiprocessors. The main idea is to represent available processors in the system by means of a prime cube graph (PC-graph). The PC-graph maintains the inter-relationships between free subcubes and hence reduces both internal and external processor fragmentations. Their simulation results show that the PC-graph approach outperforms the existing allocation strategies by 25% to 50% under certain load conditions.

title: An Algorithm for Identification of Reduced-Order Dynamic Models of Gas Turbines
abstract: Model based approaches show a lot of advantages for fault detection and condition monitoring. Particularly, it is true in employing reduced order models for real-time parameter identification and output prediction of gas turbines. Many algorithms have been developed, but most of them focus on one-step-ahead prediction models and involve complex computation. These algorithms are not acceptable for long-term prediction and real-time condition monitoring. In this paper, an improved gradient method (dynamic gradient descent) is proposed. The idea is to take account of the dependency of prediction errors and calculate the gradient information recursively. Not only low computation expense is achieved, but the non-Gaussian errors can also be overcome when this approach is applied to estimate parameters of a reduced order gas turbine model and to improve long-term prediction

title: Prime Cube Graph Approach for Processor Allocation in Hypercube Multiprocessors