This revised and extensively expanded edition of Computability and Complexity Theory
comprises essential materials that are core knowledge in the theory of computation. The …

The Church-Turing Thesis [10, Thesis I†] asserts that all effectively computable numeric
functions are recursive and, likewise, that they can be computed by a Turing machine, or …

Computations with polynomials are at the heart of any computer algebra system and also
have many applications in engineering, coding theory, and cryptography. Generally …

This series of lectures is concerned with efficient algorithms which operate on graphs. A
graph is a structure consisting of a finite set of vertices, certain pairs of which are joined by …

Services based on new information technology offering audio and video modality are
viewed among the most important today. When users change location or device there is a …

Distance oracles are data structures that provide fast (possibly approximate) answers to
shortest-path and distance queries in graphs. The tradeoff between the space requirements …

Research done in the area of integer sorting has considerably improved the lower bound
and achieved with comparison sorting ie to[1] for a deterministic algorithms or to for a radix …

Web search engines are the most popular mean of interaction with the Web. Realizing a
search engine which scales even to such issues presents many challenges. Fast crawling …

Recently the lower bound for integer sorting has considerably improved and achieved with
comparison sorting to [1] for a deterministic algorithms or to for a radix sort algorithm in …

Sorting is one of the most fundamental computational problems, and it is known that n keys
can be sorted in O (n log n) time by any of a number of well-known sorting algorithms …