Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
Papers published on a yearly basis
Papers
More filters
10 Mar 2014
TL;DR: Novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects provide super-exponential gains while their average case complexity is within constant factors of their traditional counterparts.
Abstract: We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects.
For numbers corresponding to Catalan objects of low structural complexity our algorithms provide super-exponential gains while their average case complexity is within constant factors of their traditional counterparts.
7 citations
TL;DR: It is shown that when the authors restrict ourselves to quantified conjunctions of linear inequalities, i.e., quantified linear systems, the complexity classes collapse to polynomial time, which reinforces the importance of sentence formats from the perspective of computational complexity.
7 citations
TL;DR: A p-measure is defined as a measure for which Blum's axioms can be proved in a given axiomatic system and it is shown that the complexity class of a p-function contains only p-functions and that all p- functions form a single complexity class.
7 citations
06 Jul 2009
TL;DR: It is proved that there exists a 3-argument function f whose communication complexity is *** (n) but partition arguments can only yield an *** (log n ) lower bound, and this holds for nondeterministic communication complexity and randomized communication complexity.
Abstract: Consider the "Number in Hand" multiparty communication complexity model, where k players P 1 ,...,P k holding inputs $x_1,\ldots,x_k\in{0, 1}^n$ (respectively) communicate in order to compute the value f (x 1 ,...,x k ). The main lower bound technique for the communication complexity of such problems is that of partition arguments : partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of the partition arguments method. Our two main results are very different in nature:
(i) For randomized communication complexity we show that partition arguments may be exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is *** (n ) but partition arguments can only yield an *** (log n ) lower bound. The same holds for nondeterministic communication complexity.
(ii) For deterministic communication complexity, we prove that finding significant gaps, between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on (a generalized version of) the "log rank conjecture" of communication complexity.
7 citations
TL;DR: It is shown that if P ≠ NP, then the computational complexity of H (and of similar SR-functionals) is inherently infeasible, and that when added to PCF, it yields a language that computes exactly SR.
7 citations