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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.
The Diffie and Hellman model of a Public Key Cryptosystem has received much attention as a way to provide secure network communication. In this paper, we show that the original Diffie and Hellman model does not guarantee security against other users in the system. It is shown how users, which are more powerful adversarys than the traditionally considered passive eavesdroppers, can decrypt other users...
The main results of this paper are an O(n3) probabilistic algorithm and an O(n3 log n) deterministic algorithm that test whether two given trivalent graphs are isomorphic. In fact, the algorithms construct the set of all isomorphisms of the two graphs. Variants of these algorithms construct the set of all automorphisms of a trivalent graph. The algorithms make use of some new improved permutation...
We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an...
The classical mover's problem is the following: can a rigid object in 3-dimensional space be moved from one given position to another while avoiding obstacles? It is known that a more general version of this problem involving objects with movable joints is PSPACE-complete, even for a simple tree-like structure. In this paper, we investigate a 2-dimensional mover's problem in which the object being...
Let P be a simple polygon with N vertices, each being assigned a weight ∈ {0,1}, and let C, the weight of P, be the added weight of all vertices. We prove that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3. This computation assumes that all the vertices...
We present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such that, if m(I) denotes the number of distinct sizes of...
The purpose of this paper is to introduce a new information theory and explore its appplications. Using modern computational complexity, we study the notion of information that can be accessed through a feasible computation. In Part 1 of this paper, we lay the foundation of the theory and set up a framework for cryptography and pseudorandom number generation. In Part 2, we study the concept of trapdoor...
An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's...
We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time. Both the data structure and the query algorithm are easy to implement.
Suppose it is known that {X0, X1,...,Xn} is produced by a pseudo-random number generator of the form Xi+1 = aXi + b mod m, but a, b, and m are unknown. Can one efficiently predict the remainder of the sequence with knowledge of only a few elements from that sequence? This question is answered in the affirmative and an algorithm is given.
Linear-time for Linear Programming in R2 and R3 are presented. The methods used are applicable for some other problems. For example, a linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane. This disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time. An immediate consequence of the main result is...
This paper deals with the complexity of context-free grammars with 1-1etter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is Σ2p- complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in PSPACE, solving an open problem stated...
A complexity theory for unbounded fan-in parallelism is developed where the complexity measure is the simultaneous measure (number of processors, parallel time). Two models of unbounded fan-in parallelism are (1) parallel random access machines that allow simultaneous reading from or writing to the same common memory location, and (2) circuits containing AND's, OR's and NOT's with no bound placed...
We assume that long wires represent large capacitive loads, and investigate the effect on the area of a VLSI layout when drivers are introduced along many long wires in the layout. We present a layout for which the introduction of drivers along long wires squares the area of the layout; we show, however, that the increase in area is never greater than this, if the driver can be laid out in a square...
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