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Dynamic Programming (DP) is an important and popular method for solving a wide variety of discrete optimization problems such as scheduling, string-editing, packaging, and inventory management. DP breaks problems into simpler subproblems and combines their solutions into solutions to original ones. This paper focuses on one type of dynamic programming called Nonserial Polyadic Dynamic Programming (NPDP). To run NPDP applications efficiently on an emerging General-Purpose Graphic Processing Unit (GPGPU), the authors have to exploit more parallelism to fully utilize the computing power of the hundreds of processing units in it. However, the parallelism degree varies significantly in different phases of the NPDP applications. To address the problem, the authors propose a method that can adjust the thread-level parallelism to provide a sufficient and steadier parallelism degree for different phases. If a phase has insufficient parallelism, the authors split threads into subthreads. On the other hand, the authors can limit the total number of threads in a phase by merging threads. The authors also examine the difference between the conventional problem of finding the minimum on a GPU and the NPDP-featured problem of finding the minimums of many independent sets on a GPU. Finally, the authors examine how to design an appropriate data structure to apply the memory coalescing optimization technique. The experimental results demonstrate our method can obtain the best speedup of 13.40 over the algorithm published previously.

A uniform dependence algorithm can be represented by an index set of index poinrs and a finite scl of data dcpcndcncc vectors. Usually, the convex hull R of thc index set is a nondcgcnerated convex polytope in 72". In this paper, we show that finding an optimal linear schedule for a uniform dependencc algorithm with an arbilrary bounded convex index set is equivalent lo linding a vector of smallcst norm, where the vcctor norm is defined on a symmelric convex set R ' (which is the dual of difference body R -R ) . A linear programming problem is derived for finding the smallest vector. This problem can be solved in the empirical average lime complexity 0(36n3 + 12an2 + a ) , where a is the number of the linear inequalities defining the convex hull R and n is the dimension of the index set. This lime complexity is bettcr than those of the existing methods.

ÐIn this paper, we propose an enumeration method to check link conflicts in the mapping of n-dimensional uniform dependence algorithms with arbitrary convex index sets into k-dimensional processor arrays. Previous methods on checking the link conflicts had to examine either the whole index set or the I/O spaces whose size are yx Pn or yx nÀI , respectively, where x is the problem size of the n-dimensional uniform dependence algorithm. In our approach, checking the link conflicts is done by enumerating integer solutions of a mixed integer linear program. In order to enumerate integer solutions efficiently, a representation of the integer solutions is devised so that the size of the space enumerated is yPx nÀk. Thus, our approach to checking link conflicts has better performance than previous methods, especially for larger k. For the special case k n À P, we show that link conflicts can be checked by solving two linear programs in one variable.

SUMMARYA vertex subset F ⊆ V(G) is called a cyclic vertex-cut set of a connected graph G if G − F is disconnected such that at least two components in G − F contain cycles. The cyclic vertex connectivity is the cardinality of a minimum cyclic vertex-cut set. In this paper, we show that the cyclic vertex connectivity of the trivalent Cayley graphs TG n is equal to eight for n ≥ 4.