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.

“Polynomial Time Verification of Decentralized Diagnosability of Discrete Event Systems” Versus “Decentralized Failure Diagnosis of Discrete Event Systems”: A Critical Appraisal

Abstract: In [1] , the authors claim that there is an oversight in [2] , in the sense that the proposed verifier is, in general, nondeterministic and the computational complexity analysis is incorrect. The authors in [1] also claim that the complexity of the verification algorithm presented in [3] is reduced when considering the more restrictive setting of projection masks, in contrast to the more general non-projection masks case, and equals the complexity of the verification algorithm presented in [2] . In this note, we show that the computational complexity analysis of [2] is actually correct and that the complexity of the verification algorithm presented in [3] is not reduced without additional modification of the algorithm (not yet proposed in the literature) if projection masks are used, and, therefore, is not equal to the complexity of the algorithm presented in [2] .

Decision trees and downward closures

Abstract: The separation of small complexity classes is considered. Some downward closure results are derived which show that some intuitively arrive at results that were published previously are misleading. This is done by giving uniform versions of simulations in the decision-tree model of concrete complexity. The results also show that sublinear-time computation has enough power to code interesting questions in polynomial-time complexity. >

An efficient algorithm for hidden surface removal

Abstract: We give an efficient, randomized hidden surface removal algorithm, with the best time complexity so far. A distinguishing feature of this algorithm is that the expected time spent by this algorithm on junctions which are at the "obstruction level" l, with respect to the viewer, is inversely proportional to l. This provably holds for any input, regardless of the way in which faces are located in the scene, because the expectation is with respect to randomization in the algorithm, and does not depend on the input. In practice, this means that the time complexity is roughly proportional to the size of the actually visible output times logarithm of the average depth complexity of the scene (this logarithm is very small generally).