An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Program

In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = u^k implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. Many efficient algorithms to test if a given string is square-free, have been developed so far. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n^2; n log^2 N))-time O(n^2)-space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program (BSLP). We remark that BSLP has exponential compression, that is, N = O(2^n). Hence no decompress-then-test approaches can be better than our method in the worst case

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms

Combinatorics, Probability and Computing

The main theme of this workshop was the use of probabilistic methods in combinatorics and theoretical computer science. Although these methods have been around for decades, they are being refined all the time: they are getting more and more sophisticated and powerful. Another theme was the study of random combinatorial structures, either for their own sake, or to tackle extremal questions. The workshop also emphasized connections between probabilistic combinatorics and discrete probability

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

National Educators' Workshop: Update 1989 Standard Experiments in Engineering Materials Science and Technology

Presented here is a collection of experiments presented and demonstrated at the National Educators' Workshop: Update 89, held October 17 to 19, 1989 at the National Aeronautics and Space Administration, Hampton, Virginia. The experiments related to the nature and properties of engineering materials and provided information to assist in teaching about materials in the education community