Showing papers on "Average-case complexity published in 1982"
05 May 1982
TL;DR: The pattern which will be shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity the authors show completeness in some complexity class.
Abstract: Two complexity measures for query languages are proposed. Data complexity is the complexity of evaluating a query in the language as a function of the size of the database, and expression complexity is the complexity of evaluating a query in the language as a function of the size of the expression defining the query. We study the data and expression complexity of logical languages - relational calculus and its extensions by transitive closure, fixpoint and second order existential quantification - and algebraic languages - relational algebra and its extensions by bounded and unbounded looping. The pattern which will be shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity we show completeness in some complexity class.
1,523 citations
IBM1
TL;DR: This work considers the problem of computing the median of a bag of 2n numbers by using communicating processes, each having some of the numbers in its local memory, and gives an algorithm that is optimal up to a constant.
54 citations
03 Nov 1982
TL;DR: This work greatly simplifies two well-known lower bound proofs and demonstrates how to use Kolmogorov-Complexity in analysing proba-bilistic algorithms.
Abstract: Kolmogorov-CoMplexity has turned out to be a very useful tool in proving lower bounds [5], [6], [7]. Here we will give further applications of Kolmogorov-Complexity. Firstly we will greatly simplify two well-known lower bound proofs: (a) the n(n logn/loglog n) lower bound for on-line-multiplication, originally proven in [2], [4], (b) the n(n 2 /log n) lower bound for a time-space trade-off in sorting [9]. We will also improve this bound to n(N 2 loglog N/log N). Secondly we will demonstrate how to use Kolmogorov-Complexity in analysing proba-bilistic algorithms: (c) We analyse in an elementary way the routing algorithm for n-dimensional cubes given in [10]. 1. The concept of Kolmogorov-Complexity Let C be the class of one-dimensional Turing-machines with tape-alphabet {O,I,B}. Let U be an universal machine in C. For w 1 ,w 2 E{O,I}* define the Kolmogorov-Complexity [3] by: K(w 1 {W 2 }: =the length of the shortest o/ 1 s t r i ng (" pro gram I' J p, s uc h t hat U with input pBw2 computes wI and stops. K(w): =K(wlempty string). 45 Because one program p can only generate one word w, we have Fact I : Let w 2 E{O,l}* , then i) *{wl E{O,1}*IK(w 1 IW 2) ~n} <2 n + 1 _1 i i) (Especially) there exists a string w E{O,l}n with K(wlw 2) ~n If K(wl the empty string) =n , then w i s called a random string. Two easy consequences of Fact 1 are Fact 2: (Strings with low complexity are improbable). Let w 2 E{O,l}* be fixed and determine wI E{O,l}n by tossinq a fair coin n times, then for all c Fact 3: (Random strings are locally n almost random). Let w =w 1 w 2 w 3 E{O,l} be random. Then, with w'w 2 : =w 1 w 3 ' We need the following notation. For w: =w 1 w 1 w 2 w2"" ,w n w n Ol ·
20 citations
TL;DR: The average-case behavior of a general class of algorithms to which the method of buckets can be applied is analyzed and sufficient conditions under which an algorithm A that solves a problem P of size n in O(nk), k > 1, worst-case time, can be made to run in linear expected time.
12 citations