Algorithms and Complexity

Projects Prof. Dr. Susanne Albers

Approximation and Online Algorithms for Optimization Problems (APPOL II)

Project description

In this project we design efficient algorithms with proven worst-case performance guarantees, under strict limitations either on the running time or on the accessibility of the data. For NP-hard optimization problems, constraints on the running time can often be satisfied by approximation algorithms; the second limitation leads to the notion of on-line algorithms. The project will address its objectives focusing on both traditional pardigmatic problems (graph theoretical, scheduling and packing problems) and algorithmic problems arising in new information technologies (resource management, communication and data management, telecommunication and other areas). Project Objectives Much of the theoretical research of the 1970's consisted in a classification of decision problems as either solvable exactly in polynomial time, or NP-complete. Similarly, the main effort of current algorithmic research is in classifying optimization problems according to how well they can be approximated in polynomial time. This classification is our first (theoretical) long-term objective. To this end the project will focus on identifying cornerstone problems, finding reductions among them and understanding the combinatorial structures that lead to efficient approximation algorithms. For on-line problems, the current priority concerns a critical revision and empirical validation of its basic premises, modeling assumptions and algorithmic techniques. More concretely, in terms of foundations and techniques, the specific areas that we plan to work on are: -- extensions of rounding methods for approximation schemes; -- semi-definite programming; -- the possibilities of random sampling methods for approximation schemes; -- the access graph model for online algorithms; -- probabilistic analysis of on-line algorithms for general input distributions. In terms of specific problems, we plan to work in the following areas: -- two- and three-dimensional bin packing; -- scheduling independent tasks; -- scheduling with precedence constraints; -- graph coloring and wavelength assignment in all-optical networks; -- virtual circuits in communication networks; -- paging, fragmentation and reblocking, and prefetching; -- minimum edge coloring of multigraphs, and minimum vertex cover; -- Data mining. Exploiting this theory to tackle real world applications is the second (practical) main objective of the project. The theoretically proven algorithms will be used as core algorithmic ideas that reflect the combinatorial structure of problems but need to be fine-tuned to the types of instances arising in specific applications to lead to practical algorithmic tools. Thus, there is a need for implementing and experimenting with the algorithms developed. The feedback from empirical experimentation is also at the basis of the critical revision of theoretical models and design techniques of approximation and on-line algorithms.

Start/End of project

01.11.2001 until 31.10.2004

Project manager

Prof. Dr. Susanne Albers

Contact person

Prof. Dr. Susanne Albers


Universität zu Kiel, Germany Technische Universität Berlin, Germany Universität Dortmund, Germany Université d'Evry, France Université de Paris-Sud, France Technical University of Athens, Greece Athens University, Greece Universita di Roma, Italy Teach. Training College Szeged, Hungary Maastricht University, Netherlands Technion Haifa, Israel Tel-Aviv University, Israel ETH Zürich, Switzerland