#ComputationalComplexity

[asadmukhtarr]

"Introduction to the Theory of Computation" by Michael Sipser is a foundational textbook that explores the mathematical underpinnings of computer science. By reading this book, you will gain a deep understanding of computation, its limits, and its capabilities. Below is a step-by-step breakdown of the outcomes you can expect from studying this book:

[marlamagka]

A tweet

A comparison between #deeplearning and brain function #computationalcomplexity #dendriticspikes #highperformancecomputing https://t.co/7ADrgtdP6P

— Despoina Magka (@MarlaMagka) September 7, 2018

[nvas]

I/O Complexity

Today I came across a very interesting post on I/O Complexity, an additional way of characterizing the complexity of a computation. The following abstract, to tease you out, is from Robert Harper's Existential Type blog (his full article is here). Relevant is the slideshow on Cache- and IO-Efficient Functional Algorithms.

This summer Guy Blelloch and I began thinking about other characterizations of the complexity of programs besides the familiar abstractions of execution time and space requirements of a computation.  One important measure, introduced by Jeff Vitter, is called I/O Complexity.  It measures the efficiency of algorithms with respect to memory traffic, a very significant determiner of performance of programs.  The model is sufficiently abstract as to encompass several different interpretations of I/O complexity.  Basically, the model assumes an unbounded main memory in which all data is ultimately stored, and considers a cache of  blocked into chunks of size  that provides quick access to main memory.  The complexity of algorithms is analyzed in terms of these parameters, under the assumption that in-cache accesses are cost-free, so that the only significant costs are those incurred by loading and flushing the cache.  You may interpret the abstract concepts of main memory and cache in the standard way as a two-level hierarchy representing, say, on- and off-chip memory access, or instead as representing a disk (or other storage medium) loaded into memory for processing.  The point is that the relative costs of processing cached versus uncached data is huge, and worth considering as a measure of the efficiency of an algorithm.

[marlamagka]

via Twitter https://twitter.com/MarlaMagka