Directed Bipartite Graphs Containing Every Possible Pair of Directed Cycles

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: 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 Quadrilaterals and Cycle Covers in a Bipartite Graph

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: Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model
abstract: The task of robust fault detection and diagnosis of stochastic distribution control (SDC) systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Convergency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demonstrate the effectiveness of the proposed algorithm.

title: Minimizing Area Cost of On-Chip Cache Memories by Caching Address Tags
abstract: This paper presents a technique for minimizing chip-area cost of implementing an on-chip cache memory of microprocessors. The main idea of the technique is Caching Address Tags, or CAT cache, for short. The CAT cache exploits locality property that exists among addresses of memory references. By keeping only a limited number of distinct tags of cached data, rather than having as many tags as cache lines, the CAT cache can reduce the cost of implementing tag memory by an order of magnitude without noticeable performance difference from ordinary caches. Therefore, CAT represents another level of caching for cache memories. Simulation experiments are carried out to evaluate performance of CAT cache as compared to existing caches. Performance results of SPEC92 programs show that the CAT cache, with only a few tag entries, performs as well as ordinary caches, while chip-area saving is significant. Such area saving will increase as the address space of a processor increases. By allocating the saved chip-area for larger cache capacity, or more powerful functional units, CAT is expected to have a great impact on overall system performance.

title: CPR: Composable performance regression for scalable multiprocessor models
abstract: Uniprocessor simulators track resource utilization cycle by cycle to estimate performance. Multiprocessor simulators, however, must account for synchronization events that increase the cost of every cycle simulated and shared resource contention that increases the total number of cycles simulated. These effects cause multiprocessor simulation times to scale superlinearly with the number of cores. Composable performance regression (CPR) fundamentally addresses these intractable multiprocessor simulation times, estimating multiprocessor performance with a combination of uniprocessor, contention, and penalty models. The uniprocessor model predicts baseline performance of each core while the contention models predict interfering accesses from other cores. Uniprocessor and contention model outputs are composed by a penalty model to produce the final multiprocessor performance estimate. Trained with a production quality simulator, CPR is accurate with median errors of 6.63, 4.83 percent for dual-, quad-core multiprocessors. Furthermore, composable regression is scalable, requiring 0.33x the simulations required by prior regression strategies.

title: A scalable associative processor with applications in database and image processing
abstract: This paper describes the implementation and use of a dedicated associative SIMD coprocessor ideally suited for many applications such as database processing, image processing, genome matching, or molecular similarity analysis. The concept of associative SIMD processing is introduced, and differentiated from other associative and SIMD techniques. Then our ASC (associative computing) processor is briefly described, along with its implementation of associative SIMD processing. Finally, we demonstrate the use of our ASC processor on relational database processing and on the image processing operation of edge detection.

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.