14 research outputs found
Discrete Convex Functions on Graphs and Their Algorithmic Applications
The present article is an exposition of a theory of discrete convex functions
on certain graph structures, developed by the author in recent years. This
theory is a spin-off of discrete convex analysis by Murota, and is motivated by
combinatorial dualities in multiflow problems and the complexity classification
of facility location problems on graphs. We outline the theory and algorithmic
applications in combinatorial optimization problems
Machine speed scaling by adapting methods for convex optimization with submodular constraints
In this paper, we propose a new methodology for the speed-scaling problem based on its link to scheduling with controllable processing times and submodular optimization. It results in faster algorithms for traditional speed-scaling models, characterized by a common speed/energy function. Additionally, it efficiently handles the most general models with job-dependent speed/energy functions with single and multiple machines. To the best of our knowledge, this has not been addressed prior to this study. In particular, the general version of the single-machine case is solvable by the new technique in O(n2) time
Faster Algorithms for Mean-payoff Games
In this paper, we study algorithmic problems for quantitative models that are motivated by the applications in modeling embedded systems. We consider two-player games played on a weighted graph with mean-payoff objective and with energy constraints. We present a new pseudopolynomial algorithm for solving such games, improving the best known worst-case complexity for pseudopolynomial mean-payoff algorithms. Our algorithm can also be combined with the procedure by Andersson and Vorobyov to obtain a randomized algorithm with currently the best expected time complexity. The proposed solution relies on a simple fixpoint iteration to solve the log-space equivalent problem of deciding the winner of energy games. Our results imply also that energy games and mean-payoff games can be reduced to safety games in pseudopolynomial time. © 2010 Springer Science+Business Media, LLC.SCOPUS: ar.jinfo:eu-repo/semantics/publishe