Final Report Summary - PAAL (Practical Approximation Algorithms)
The goal of this proposal is the development and study of practical approximation algorithms. We base our study on theoretical models that can describe requirements for algorithms that make them practically efficient. Our research on approximation algorithms is concentrated
around the following four main aspects:
- Pricing problems with many budget constraints – we have given efficient algorithms for auctions with budgeted agents.
- Multi-problem optimization, when the solution has to be composed out of different problems that need to interact – we have abstracted several types of such problems, where layers are composed by taking unions and intersection, and we have given efficient approximation algorithms for such problem.
- Efficient approximation algorithms captured by dynamic and pre-processing models – we have succeeded in giving efficient dynamic and pre-processing algorithms for maxflow, min-cut and Steiner tree problems; we have introduced graph timelines a new pre-processing framework for graph algorithms.
- Interplay between regular and random structures of networks – we have studied network properties that allow for development of efficient approximation algorithms, e.g. we have created a new deterministic notion of power law graphs.
The above theoretical work was accompanied by studying practical efficiently of these solutions, and generic programming concepts for them. The created algorithms are available here: http://paal.mimuw.edu.pl.
around the following four main aspects:
- Pricing problems with many budget constraints – we have given efficient algorithms for auctions with budgeted agents.
- Multi-problem optimization, when the solution has to be composed out of different problems that need to interact – we have abstracted several types of such problems, where layers are composed by taking unions and intersection, and we have given efficient approximation algorithms for such problem.
- Efficient approximation algorithms captured by dynamic and pre-processing models – we have succeeded in giving efficient dynamic and pre-processing algorithms for maxflow, min-cut and Steiner tree problems; we have introduced graph timelines a new pre-processing framework for graph algorithms.
- Interplay between regular and random structures of networks – we have studied network properties that allow for development of efficient approximation algorithms, e.g. we have created a new deterministic notion of power law graphs.
The above theoretical work was accompanied by studying practical efficiently of these solutions, and generic programming concepts for them. The created algorithms are available here: http://paal.mimuw.edu.pl.