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.

On Distributed Time-Dependent Shortest Paths over Duty-Cycled Wireless Sensor Networks

Abstract: We revisit the shortest path problem in asynchronous duty-cycled wireless sensor networks, which exhibit time-dependent features. We model the time-varying link cost and distance from each node to the sink as periodic functions. We show that the time-cost function satisfies the FIFO property, which makes the time-dependent shortest path problem solvable in polynomial-time. Using the $\beta$-synchronizer, we propose a fast distributed algorithm to build all-to-one shortest paths with polynomial message complexity and time complexity. The algorithm determines the shortest paths for all discrete times with a single execution, in contrast with multiple executions needed by previous solutions. We further propose an efficient distributed algorithm for time-dependent shortest path maintenance. The proposed algorithm is loop-free with low message complexity and low space complexity of $O(maxdeg)$, where $maxdeg$ is the maximum degree for all nodes. The performance of our solution is evaluated under diverse network configurations. The results suggest that our algorithm is more efficient than previous solutions in terms of message complexity and space complexity.

A high performance, low complexity algorithm for compile-time job scheduling in homogeneous computing environments

Abstract: Efficient job scheduling is one of the most important and difficult issues in homogeneous computing environments. List-scheduling is generally accepted as an attractive static approach, since it pairs low complexity with good results. This paper presents a static list-scheduling algorithm with a limited number of processors. The algorithm is called critical nodes parent trees (CNPT). The aim of the algorithm is to give results comparable to or better than the current algorithms, and to achieve very low complexity. The experimental work has shown that the suggested algorithm gave comparable results in a low complexity.

Complexity of computations

Abstract: The framework for research in the theory of complexity of computations is described, emphasizing the interrelation between seemingly diverse problems and methods. Illustrative examples of practical and theoretical significance are given. Directions for new research are discussed.

On the average-case complexity of MCSP and its variants

Abstract: We prove various results on the complexity of MCSP (Minimum Circuit Size Problem) and the related MKTP (Minimum Kolmogorov Time-Bounded Complexity Problem):• We observe that under standard cryptographic assumptions, MCSP has a pseudorandom self-reduction. This is a new notion we define by relaxing the notion of a random self-reduction to allow queries to be pseudorandom rather than uniformly random. As a consequence we derive a weak form of a worst-case to average-case reduction for (a promise version of) MCSP. Our result also distinguishes MCSP from natural NP-complete problems, which are not known to have worst-case to average-case reductions. Indeed, it is known that strong forms of worst-case to average-case reductions for NP-complete problems collapse the Polynomial Hierarchy.• We prove the first non-trivial formula size lower bounds for MCSP by showing that MCSP requires nearly quadratic-size De Morgan formulas.• We show average-case superpolynomial size lower bounds for MKTP against AC0[p] for any prime p.• We show the hardness of MKTP on average under assumptions that have been used in much recent work, such as Feige's assumptions, Alekhnovich's assumption and the Planted Clique conjecture. In addition, MCSP is hard under Alekhnovich's assumption. Using a version of Feige's assumption against co-nondeterministic algorithms that has been conjectured recently, we provide evidence for the first time that MKTP is not in coNP. Our results suggest that it might worthwhile to focus on the average-case hardness of MKTP and MCSP when approaching the question of whether these problems are NP-hard.

Measuring dynamic program complexity

Abstract: A relative complexity technique that combines the features of many complexity metrics to predict performance and reliability of a computer program is presented. Relative complexity aggregates many similar metrics into a linear compound metric that describes a program. Since relative complexity is a static measure, it is expanded by measuring relative complexity over time to find a program's functional complexity. It is shown that relative complexity gives feedback on the same complexity domains that many other metrics do. Thus, developers can save time by choosing one metric to do the work of many. >