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.

Path planning by optimal-path-map construction for homogeneous-cost two-dimensional regions

Abstract: Algorithms to construct optimal-path maps for single isolated homogeneous-cost convex-polygonal regions are discussed. Assuming the ability to construct optimal paths for a certain set of key points, a complete analysis is given of one of the four possible single-region situations, showing how to partition the map into regions of similar path behavior. An algorithm is then proposed for constructing optimal-path maps for multiple such regions, in the case that they meet certain decomposability constraints. This algorithm is of O(n/sup 4/) time complexity and O(n) space complexity, where n is the number of vertices in a polygonal model of the terrain as homogeneous-cost regions. The algorithm greatly simplifies planning of paths through areas of terrain with near-uniform characteristics, allowing a robot to exploit optimal paths but still have significant time for other matters. >

Amortized communication complexity

Abstract: The authors study the direct sum problem with respect to communication complexity: Consider a function f: D to (0, 1), where D contained in (0, 1)/sup n/*(0, 1)/sup n/. The amortized communication complexity of f, i.e. the communication complexity of simultaneously computing f on l instances, divided by l is studied. The authors present, both in the deterministic and the randomized model, functions with communication complexity Theta (log n) and amortized communication complexity O(1). They also give a general lower bound on the amortized communication complexity of any function f in terms of its communication complexity C(f). >

Oracles Are Subtle But Not Malicious

Abstract: Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from trying to solve those problems. First, we give an oracle relative to which PP has linear-sized circuits, by proving a new lower bound for perceptrons and low-degree threshold polynomials. This oracle settles a longstanding open question, and generalizes earlier results due to Beigel and to Buhrman, Fortnow, and Thierauf. More importantly, it implies the first provably nonrelativizing separation of "traditional" complexity classes, as opposed to interactive proof classes such as MIP and MA/sub EXP/. For Vinodchandran showed, by a nonrelativizing argument, that PP does not have circuits of size n/sup k/ for any fixed k. We present an alternative proof of this fact, which shows that PP does not even have quantum circuits of size n/sup k/ with quantum advice. To our knowledge, this is the first nontrivial lower bound on quantum circuit size. Second, we study a beautiful algorithm of Bshouty et al. for learning Boolean circuits in ZPP/sup NP/. We show that the NP queries in this algorithm cannot be parallelized by any relativizing technique, by giving an oracle relative to which ZPP/sup NP//sub /spl par// and even BPP/sup NP//sub /spl par// have linear-size circuits. On the other hand, we also show that the NP queries could be parallelized if P = NP. Thus, classes such as ZPP/sup NP//sub /spl par// inhabit a "twilight zone", where we need to distinguish between relativizing and black-box techniques. Our results on this subject have implications for computational learning theory as well as for the circuit minimization problem.

On polynomial and generalized complexity cores

Abstract: Recent results on polynomial complexity cores, their complexity, density, and structure and their counterparts on proper hard cores are surveyed and interpreted. An approach to generalized complexity cores that is almost axiomatic in nature is included in the discussion. The purpose is to provide an integrated presentation of this material. >

Real-time H.264 video encoding in software with fast mode decision and dynamic complexity control

Abstract: This article presents a novel real-time algorithm for reducing and dynamically controlling the computational complexity of an H.264 video encoder implemented in software. A fast mode decision algorithm, based on a Pareto-optimal macroblock classification scheme, is combined with a dynamic complexity control algorithm that adjusts the MB class decisions such that a constant frame rate is achieved. The average coding efficiency of the proposed algorithm was found to be similar to that of conventional encoding operating at half the frame rate. The proposed algorithm was found to provide lower average bitrate and distortion than static complexity scaling.