广义二叉树的Huang和Wong算法

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2022-02-14 DOI:10.1007/s00236-021-00411-z

Marek Chrobak, Mordecai Golin, J. Ian Munro, Neal E. Young

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引用次数: 5

摘要

Huang和Wong (Acta Inform 21(1): 113-123, 1984)提出了一种计算最优广义二叉树的多项式时间动态规划算法。我们证明他们的算法是不正确的。因此，能否在多项式时间内计算出这样的树仍然是一个开放的问题。Spuler(使用双向键比较的最优搜索树，博士论文，1994)提出修改Huang和Wong的算法，得到一个不同问题的算法:计算最优双向比较搜索树。我们证明了基于Spuler算法的动态规划是无效的，因为它不满足必要的最优子结构性质，它所提出的递推关系是不正确的。目前尚不清楚该算法是否保证计算出正确的整体解。

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On Huang and Wong’s algorithm for generalized binary split trees

Huang and Wong (Acta Inform 21(1):113–123, 1984) proposed a polynomial-time dynamic-programming algorithm for computing optimal generalized binary split trees. We show that their algorithm is incorrect. Thus, it remains open whether such trees can be computed in polynomial time. Spuler (Optimal search trees using two-way key comparisons, PhD thesis, 1994) proposed modifying Huang and Wong’s algorithm to obtain an algorithm for a different problem: computing optimal two-way comparison search trees. We show that the dynamic program underlying Spuler’s algorithm is not valid, in that it does not satisfy the necessary optimal-substructure property and its proposed recurrence relation is incorrect. It remains unknown whether the algorithm is guaranteed to compute a correct overall solution.

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来源期刊

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.