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We report on a symbolic-numeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient...
An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.
We examine the possibility of translating an attribute system into a recursive program scheme taking derivation trees as arguments. This is possible if and only if the attribute system is strongly non-circular. The strong non circularity is decidable in polynomial time. Our recursive program schemes allow us to attack the equivalence problem for attribute systems and solve it in a special case properly...
Canonical labelling of graphs (CL, for short) can be used, e.g., to test isomorphism. We prove that a simple vertex classification procedure results after only two refinement steps in a CL of random graphs with probability 1 - exp(-cn). With a slight modification we obtain a linear time CL algorithm with only exp(-cn log n/log log n) probability of failure. An additional depth-first search yields...
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