, Algorithms for Drawing Planar Graphs, PhD thesis, Univ. of Utrecht, 1993. Home/Search Document Details and Download
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Testing Membership in Unitriangular Matrix Groups - Ivanyos (1996) (Correct)
....for computational problems in some classes of matrix groups over algebraic number fields have been recently obtained. The constructive membership problem in a linear group G given by a finite set of generators has been shown to be soluble in polynomialtime in the one dimensional case by Ge [Ge1, Ge2], in the abelian case by Cai, Lipton, Zalcstein [CLZ] Babai, Beals, Cai, Ivanyos, and Luks [BBCIL] in the abelian by finite case by Beals [Be] Beals [Be] also presents a polynomial time algorithm that decides whether G is soluble by finite (nilpotent by finite, or abelian by finite) and if ....
G. Ge: Algorithms related to multiplicative representations of algebraic numbers, PhD thesis, Math Dept, U. C. Berkeley, 1993.
Algorithms for matrix groups and the Tits alternative - Beals (1995) (4 citations) (Correct)
.... for several classes of finite matrix groups have been obtained in the last few years [Lu92, BBR, BB] Some important complexity results for these groups were obtained ten years ago [BSz, Ba85] For infinite matrix groups, polynomial time algorithms are known only for the class of abelian groups [KLi, Ge93a, Ge93b, CLZ, BBCIL]. This research has benefited theoretical computer science in several ways. One of the motivations for the invention of interactive proofs was Babai s investigation of complexity in finite matrix groups [Ba85] Much of our understanding of the complexity of graph isomorphism comes from research in ....
....Also, Babai, Beals, and Rockmore [BBR] have given a deterministic polynomial time algorithm to test finiteness. For abelian groups, Babai, Beals, Cai, Ivanyos, and Luks [BBCIL] give deterministic algorithms for both problems, building on work of Cai, Lipton, and Zalcstein [CLZ] and Ge [Ge93a, Ge93b] (G. Ostheimer [Os] has developed similar methods independently) We extend both of these lines of research, giving Las Vegas algorithms for groups with abelian subgroups of finite index. We obtain weaker results for two larger classes of groups: those with a nilpotent subgroup of finite index, ....
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G. Ge: Algorithms related to multiplicative representations of algebraic numbers, PhD thesis, Math Dept, U. C. Berkeley, 1993.
Compact Encodings of Planar Graphs via Canonical.. - Chuang, Garg, He, Kao.. (1998) (16 citations) Self-citation (Graphs) (Correct)
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, Algorithms for Drawing Planar Graphs, PhD thesis, Univ. of Utrecht, 1993.
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