Pentagons and cycle coverings
Let G be a graph of order n ≥ 5k + 2, where k is a positive integer. Suppose that the minimum degree of G is at least (n + k)/2 . We show that G contains k pentagons and a path such that they are vertexdisjoint and cover all the vertices of G. Moreover, if n ≥ 5k + 7, then G contains k + 1 vertex-disjoint cycles covering all the vertices of G such that k of them are pentagons.

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: 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: 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: 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: Processor Performance Modeling using Symbolic Simulation
abstract: We propose a method of analytically characterizing processor performance as a function of circuit latencies. In our approach, we modify traditional simulation to use variables instead of fixed latencies for the internal functional units. The simulation engine then algebraically computes execution times, and the result is a mathematical equation which characterizes the performance space across numerous processor configurations. We discuss the computational complexity issues of this approach and show that instruction chunking and simple equation redundancy checking can make this approach feasible-we can model a large multi-dimensional design space with thousands to millions of design parameter combinations for about 10times the simulation time of a single conventional simulation run. We demonstrate our approach by exploring two different machines: a traditional MlPS-style in-order pipeline and the Intel Graphics

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: Minimum entropy of B-spline PDF systems with mean constraint
abstract: For the B-spline approximation of the continuous probability density function (PDF), the relationships between the B-spline weights and entropy both in general and under the mean constraint have been analyzed. It provides the conditions under which the minimum entropy can be achieved subject to the mean constraint. The difference between the entropy of continuous and discrete distributions has also been clarified. A minimum entropy controller with the mean constraint is then developed and several simulations are performed to verify the main results.

title: Adaptive Tracking Control for the Output PDFs Based on Dynamic Neural Networks
abstract: In this paper, a novel adaptive tracking control strategy is established for general non-Gaussian stochastic systems based on two-step neural network models. The objective is to control the conditional PDF of the system output to follow a given target function by using dynamic neural network models. B-spline neural networks are used to model the dynamic output probability density functions (PDFs), then the concerned problem is transferred into the tracking of given weights corresponding to the desired PDF. The dynamic neural networks with undetermined parameters are employed to identify the nonlinear relationships between the control input and the weights. To achieve control objective, an adaptive state feedback controller is given to estimate the unknown parameters and control the nonlinear dynamics.

title: Register renaming and scheduling for dynamic execution of predicated code
abstract: To achieve higher processor performance requires greater synergy between advanced hardware features and innovative compiler techniques. Recent advancement in compilation techniques for predicated execution has provided significant opportunity in exploiting instruction level parallelism. However, little research has been done on how to efficiently execute predicated code in a dynamic microarchitecture. In this paper, we evaluate hardware optimizations for executing predicated code on a dynamically scheduled microarchitecture. We provide two novel ideas to improve the efficiency of executing predicated code. On a generic Intel Itanium processor pipeline model, we demonstrate that, with some microarchitecture enhancements, a dynamic execution processor can achieve about 16% performance improvement over an equivalent static execution processor.