Isomorphic Strategy for Processor Allocation in k-Ary n-Cube Systems

Due to its topological generality and flexibility, the k-ary n-cube architecture has been actively researched for various applications. However, the processor allocation problem has not been adequately addressed for the k-ary n-cube architecture, even though it has been studied extensively for hypercubes and meshes. The earlier k-ary n-cube allocation schemes based on conventional slice partitioning suffer from internal fragmentation of processors. In contrast, algorithms based on job-based partitioning alleviate the fragmentation problem but require higher time complexity. This paper proposes a new allocation scheme based on isomorphic partitioning, where the processor space is partitioned into higher dimensional isomorphic subcubes. The proposed scheme minimizes the fragmentation problem and is general in the sense that any size request can be supported and the host architecture need not be isomorphic. Extensive simulation study reveals that the proposed scheme significantly outperforms earlier schemes in terms of mean response time for practical size k-ary and n-cube architectures. The simulation results also show that reduction of external fragmentation is more substantial than internal fragmentation with the proposed scheme

Isomorphic Strategy for Processor Allocation in k-Ary n-Cube Systems

Due to its topological generality and flexibility, the k-ary n-cube architecture has been actively researched for various applications. However, the processor allocation problem has not been adequately addressed for the k-ary n-cube architecture, even though it has been studied extensively for hypercubes and meshes. The earlier k-ary n-cube allocation schemes based on conventional slice partitioning suffer from internal fragmentation of processors. In contrast, algorithms based on job-based partitioning alleviate the fragmentation problem but require higher time complexity. This paper proposes a new allocation scheme based on isomorphic partitioning, where the processor space is partitioned into higher dimensional isomorphic subcubes. The proposed scheme minimizes the fragmentation problem and is general in the sense that any size request can be supported and the host architecture need not be isomorphic. Extensive simulation study reveals that the proposed scheme significantly outperforms earlier schemes in terms of mean response time for practical size k-ary and n-cube architectures. The simulation results also show that reduction of external fragmentation is more substantial than internal fragmentation with the proposed scheme

Processor allocation in k-ary n-cube multiprocessors

[[abstract]]Composed of various topologies, the k-ary n-cube system is desirable for accepting and executing topologically different tasks. We propose a new allocation strategy to utilize the large amount of processor resources in the k-ary n-cubes. Our strategy is an extension of the TC strategy on hypercubes and is able to recognize all subcubes with different topologies. Simulation results show that with such full subcube recognition ability and no internal fragmentation, our strategy depicts constantly better performance than other strategies, such as the Free list strategy on k-ary n-cubes and the Sniffing strategy[[sponsorship]]台灣大學[[conferencetype]]國際[[conferencedate]]19971218~19971220[[conferencelocation]]臺北市, 臺

Processor Allocation in K-Ary N-Cube Multiprocessors

[[abstract]]Composed of various topologies, the k-ary n-cube system is desirable for accepting and executing topologically different tasks. In this paper, we propose a new allocation strategy to utilize the large amount of processor resources in the k-ary n-cubes. Our strategy is an extension of the TC strategy on hypercubes and is able to recognize all subcubes with different topologies. Simulation results show that with such full subcube recognition ability and no internal fragmentation, our strategy depicts constantly better performance than the other strategies, such as the Free-list strategy on k- ary n-cubes and the Sniffing strategy.[[sponsorship]]台灣大學[[conferencetype]]國內[[conferencedate]]19971218~19971220[[booktype]]紙本[[iscallforpapers]]Y[[conferencelocation]]臺北市, 臺

Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications

Multi-Terminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of high-level model description techniques. However, this type of Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0-assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zero-suppressed MTBDDs and proves that they are canonical representations of multi-valued functions on finite input sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partially-shared zero-suppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the well-known standard type of MTBDDs, where both types of DDs have been implemented by us within the C++-based DD-package JINC. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multi-terminal) zero-suppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficienc

Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modelling

As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions