Limin Xiang

Efficient loopless generation of gray codes for K -array trees

Abstract Vajnovszki recently developed a loopless algorithm [Inform. Process. Lett. 68 (1998) 113] to enumerate Gray codes for binary trees, and then Korsh and Lafollette gave a loopless algorithm [Inform. Process. Lett. 70 (1999) 7] to generate Gray codes for k -ary trees. In this paper, another loopless algorithm is presented to list Gray codes for k -ary trees more efficiently in both space and time than the two former algorithms, and the algorithm is also conceptually simpler than the predecessors. Based on the algorithm, Gray codes for k -ary trees with n internal nodes ( n≥2 and k>3 ) can be generated in at least 2 2(n−1) different ways easily.

Generating regular K -ary trees efficiently

A recursive algorithm GenWordsRand a non-recursive algorithmGenWordsNRare presented in this paper to generate sequences for regular k-ary trees efficiently. They are compared with some of the previous recursive and non-recursive algorithms for this problem that were found in the literature. When the average number of recursive calls is used as a measure of the time complexity of recursive algorithms for generating k-ary trees, O(k) calls for a k-ary tree is the best result in the previous recursive algorithms, while O(1/k) calls for ak-ary tree is needed byGenWordsR. When the average number of comparisons is used as a measure of the time complexity of non-recursive algorithms for generating k-ary trees, GenWordsNRoutperforms the previous non-recursive algorithms. Ask increases, the number (and the average number) of comparisons performed by GenWordsNRtends to 66% that of the best previous non-recursive algorithms.

On generating k -ary trees in computer representation

Many algorithms have been developed to generate sequences for trees, and a few are to generate trees themselves, i.e., in computer representation. Two new algorithms are presented in this paper to generate k-ary trees in computer representation. One is recursive with constant average time per tree and the other is loopless (non-recursive) with constant time per tree. Both of them are simple and able to be understood easily.  2001 Elsevier Science B.V. All rights reserved.

Optimal intensity-modulation projection technique for three-dimensional shape measurement

A new pattern projection technique for measuring three-dimensional topography is presented, called the optimal intensity-modulation projection technique. The proposed technique dramatically shortens the measurement time and improves stripe detection accuracy compared with previous methods. Furthermore, the method deals reliably with discontinuous patterns and multiple objects.

ANSV problem on BSRs

Abstract Optimal parallel algorithms for the ANSV ( All Nearest Smaller Values ) problem are known on CREW, CRCW, and EREW PRAMs, and on the Hypercube. In this paper, optimal parallel algorithms of constant time for the ANSV problem are discussed on BSR (broadcasting with selective reduction), BSR with multiple criteria, and BSR + . The solution in this paper is the first constant time solution to the ANSV problem on any model of computation.

On time bounds, the work-time scheduling principle, and optimality for BSR

Constant time solutions for many applications have been obtained on BSR, but some theoretical problems on BSR (broadcasting with selective reduction) that raised when BSR was proposed have not been solved. Three of them are: 1) No lower bound for any problem on BSR is known except trivial constant time, 2) is there any improvement with nonconstant BSR time but still better than the lower bound for CRCW?, and 3) how to characterize problems for which BSR achieves constant time performance. In this paper, we have solved these three problems. For Problem 1, a lower bound on BSR is shown for any computational problem with an optimal sequential solution. An efficient sorting algorithm answers the second problem. A necessary condition is given for the third problem. The work-time (WT) scheduling principle and optimality for BSR are also introduced for investigating the BSR performance when the number of processors available, p, is different from the input size, n, of problems.

Decoding and drawing on BSR for a binary tree from its i-p sequence

The i-p sequence is one of the most common encodings for a binary tree. This paper gives constant time BSR parallel algorithms for the decoding and drawing of a binary tree from its i-p sequence respectively.

An efficient implementation for the BROADCAST instruction of BSR/sup +/

BSR (Broadcasting with Selective Reduction) is a PRAM more powerful than any CRCW PRAM. In order to extend the Broadcast Instruction of BSR and make it more useful for a large class of applications, this article permits it to use a general form of selection, specifically, an arbitrary relational expression. BSR with general selection is denoted by BSR/sup +/. Thus, BSR or BSR with k criteria (k>1) is BSR/sup +/ in a special case. An efficient implementation for the Broadcast Instruction of BSR/sup +/ is proposed, requiring (1/k)th of the circuits used by the best previous implementation of BSR with k criteria. Of all PRAMs, BSR/sup +/ is the most powerful in computation.

Rearranging scattered information on BSR

Abstract The problem of rearranging scattered information arises in many applications of data/information management systems. A simpler case of this problem is the so-called k-compaction problem, which requires Ω( log n ) EREW PRAM time, Ω( log log n) CREW PRAM time, or Θ(logk/log logn) CRCW PRAM time using n processors. In this paper, we give constant time parallel algorithms using n processors on BSR, another PRAM model, for the problem of rearranging scattered information and the k-compaction problem.

A theorem on the relation between BSR k amd BSR

Abstract PRAM is the most popular model of parallel computation. Of its three variants most commonly used, CREW is more powerful than EREW, and CRCW is the most powerful. BSR is another PRAM model, which is more powerful than CRCW. BSR k and BSR + are models extended from BSR, and in this paper a theorem is shown on the relation between BSR k and BSR + .