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.
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TL;DR: Probabilistic results on the quality of the origin as starting point and the average number of steps of a centering algorithm for random linear programming problems distributed according to the rotation symmetry model are presented.
2 citations
08 Oct 2012
TL;DR: This work analyzes a well-known state-of-the-art algorithm in normal system conditions, in which crash failures may occur but no malicious attacks, proving that it is fast on average and leveraging its analysis to improve its best-case complexity from three to two phases.
Abstract: Randomized Byzantine Consensus can be an interesting building block in the implementation of asynchronous distributed systems. Despite its exponential worst-case complexity, which would make it less appealing in practice, a few experimental works have argued quite the opposite. To bridge the gap between theory and practice, we analyze a well-known state-of-the-art algorithm in normal system conditions, in which crash failures may occur but no malicious attacks, proving that it is fast on average. We then leverage our analysis to improve its best-case complexity from three to two phases, by reducing the communication operations through speculative executions. Our findings are confirmed through an experimental validation.
2 citations
Book•
01 Jan 1988
TL;DR: The equivalence of dgsm replications on Q-rational languages is decidable and the learnability of DNF formulae is debated.
Abstract: Communication complexity of PRAMs.- Average case complexity analysis of the RETE multi-pattern match algorithm.- Problems easy for tree-decomposable graphs extended abstract.- Serializability in distributed systems with handshaking.- Algorithms for planar geometric models.- Nonuniform learnability.- Zeta functions of recognizable languages.- Dynamic programming on graphs with bounded treewidth.- Efficient simulations of simple models of parallel computation by time-bounded ATM's and space-bounded TM's.- Optimal slope selection.- Approximation of a trace, asynchronous automata and the ordering of events in a distributed system.- New techniques for proving the decidability of equivalence problems.- Transitive orientations, mobius functions, and complete semi-thue systems for free partially commutative monoids.- The complexity of matrix transposition on one-tape off-line turing machines with output tape.- Geometric structures in computational geometry.- Arrangements of curves in the plane - topology, combinatorics, and algorithms.- Reset sequences for finite automata with application to design of parts orienters.- Random allocations and probabilistic languages.- Systolic architectures, systems and computations.- New developments in structural complexity theory.- Operational semantics of OBJ-3.- Do we really need to balance patricia tries?.- Contractions in comparing concurrency semantics.- A complexity theory of efficient parallel algorithms.- On the learnability of DNF formulae.- Efficient algorithms on context-free graph languages.- Efficient analysis of graph properties on context-free graph languages.- A polynomial-time algorithm for subgraph isomorphism of two-connected series-parallel graphs.- Constructive Hopf's theorem: Or how to untangle closed planar curves.- Maximal dense intervals of grammar forms.- Computations, residuals, and the power of indeterminacy.- Nested annealing: A provable improvement to simulated annealing.- Nonlinear pattern matching in trees.- Invertibility of linear finite automata over a ring.- Moving discs between polygons.- Optimal circuits and transitive automorphism groups.- A Kleene-presburgerian approach to linear production systems.- On minimum flow and transitive reduction.- La Reconnaissance Des Facteurs D'un Langage Fini Dans Un Texte En Temps Lineaire - Resume -.- Regular languages defined with generalized quantifiers.- A dynamic data structure for planar graph embedding.- Separating polynomial-time turing and truth-table reductions by tally sets.- Assertional verification of a timer based protocol.- Type inference with partial types.- Some behavioural aspects of net theory.- The equivalence of dgsm replications on Q-rational languages is decidable.- Pfaffian orientations, 0/1 permanents, and even cycles in directed graphs.- On restricting the access to an NP-oracle.- On ? 1?tt p -sparseness and nondeterministic complexity classes.- Semantics for logic programs without occur check.- Outer narrowing for equational theories based on constructors.
2 citations
01 Jan 2017
TL;DR: A public-coin interactive proof system for S of round complexity O(r(n)/ logn) is shown, where logn is the number of instances of length n, and r is the randomness complexity.
Abstract: Consider an interactive proof system for some set S that has randomness complexity r(n) for instances of length n, and arbitrary round complexity. We show a public-coin interactive proof system for S of round complexity O(r(n)/ logn). Furthermore, the randomness complexity is preserved up to a constant factor, and the resulting interactive proof system has perfect completeness. 2012 ACM Subject Classification Theory of computation → Interactive proof systems
2 citations
Journal Article•
TL;DR: In this article, the authors studied the value of help bits in the settings of randomized and average-case complexity, and showed that for k at most logarithmic, the decision problem is k-membership comparable if using help bits, k instances of the problem can be efficiently solved with probability greater than 2 ǫ l 2 l-k.
Abstract: "Help bits" are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. In this paper, we study the value of help bits in the settings of randomized and average-case complexity.
If k instances of a decision problem can be efficiently solved using $${\ell < k}$$l
Amir, Beigel, and Gasarch (1990) show that for constant k, all k-membership comparable languages are in P/poly. We extend this result to the setting of randomized computation: We show that for k at most logarithmic, the decision problem is k-membership comparable if using $${\ell}$$l help bits, k instances of the problem can be efficiently solved with probability greater than $${2^{\ell-k}}$$2l-k. The same conclusion holds if using less than $${k(1 - h(\alpha))}$$k(1-h(ź)) help bits (where $${h(\cdot)}$$h(·) is the binary entropy function), we can efficiently solve $${1-\alpha}$$1-ź fraction of the instances correctly with non-vanishing probability. We note that when k is constant, k-membership comparability implies being in P/poly.
Next we consider the setting of average-case complexity: Assume that we can solve k instances of a decision problem using some help bits whose entropy is less than k when the k instances are drawn independently from a particular distribution. Then we can efficiently solve an instance drawn from that distribution with probability better than 1/2. Finally, we show that in the case where k is super-logarithmic, assuming k-membership comparability of a decision problem, one cannot prove that the problem is in P/poly by a "relativizing" proof technique. All previous known proofs in this area have been relativizing.
2 citations