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个人简介
Education
BS, 1960, City College of New York
PhD, 1966, Massachusetts Institute of Technology
Research Interests
Recent research by Professor Luks has involved the design and analysis of algorithms, with a focus on computational solutions to algebraic problems. The main objective is an understanding of the computational complexity and practical solvability of questions that can make use of algebraic structures such as groups.
Although there are many applications, a particular driving force behind the research has been the connections to problems similar to graph isomorphism. There is strong evidence that these group-theoretic problems are not NP-complete. Nevertheless, although graph isomorphism is rarely difficult in practice, it is not known to be in polynomial time. Introducing new algebraic procedures, Professor Luks's work has led to polynomial-time procedures for significant graph classes and to the best timing for general graphs.
A principal goal of current projects is improved sequential algorithms for group-theoretic problems, seeking to extend the class of algebraic problems that have efficient solutions. This involves broad investigations aimed at finding feasible (polynomial-time) solutions to problems for which only asymptotically infeasible (exponential-time) have been available. Deeper studies of certain fundamental questions is intended to improve algorithmic performance; for example, for problems involving permutation groups, timing has been improved by an order of magnitude in most basic problems and as much as four orders of magnitude for deeper structural questions; other improvements have resulted from the introduction of random methods. Furthermore, implementations have been obtained that are practically efficient while retaining their guarantee of asymptotic efficiency.
A second major effort is directed toward the parallelization of the machinery for algebraic computation. In the case of group-theoretic software, almost all the traditional programs appear to rely on inherently sequential (nonparallelizable) procedures. Thus, the parallel approach necessarily rests on entirely new foundations for computation in algebraic structures. In particular, the verification of correctness has made use of very recent breakthroughs in finite group theory. A remarkable spin-off of these new techniques has been their evident reapplication to (practically as well as asymptotically) efficient sequential computation.
There are frequent instances of applications to other domains. Recent examples include use of symmetry in constraint-satisfaction problems and application of group-theoretic tools to testing equivalence of switching circuits.
For his innovations in graph isomorphism and related issues, Professor Luks was awarded the Delbert Ray Fulkerson Prize in Discrete Mathematics by the Mathematical Programming Society and the American Mathematical Society.
研究兴趣
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Journal of Artificial Intelligence Researchno. 1 (2011): 441-531
Journal of Artificial Intelligence Researchno. 1 (2011): 481-534
ISSAC '02: Proceedings of the 2002 international symposium on Symbolic and algebraic computationno. 4 (2011): 61-96
mag(2005)
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Annals of Mathematics and Artificial Intelligenceno. 1 (2004): 19-45
AAAI'04: Proceedings of the 19th national conference on Artifical intelligencepp.55-60, (2004)
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