Approximation and online algorithms in scheduling and coloring
In the last three decades, approximation and online algorithms have become a major area of theoretical computer science and discrete mathematics. Scheduling and coloring problems are among the most popular ones for which approximation and online algorithms have been analyzed. On one hand, motivated by the well-known difficulty to obtain good lower bounds for the problems, it is particularly hard to prove results on the online and offline performance of algorithms. On the other hand, the theoretically oriented studies of approximation and online algorithms for scheduling and coloring have also impact on the development of better algorithms for real world applications. In the thesis we present approximation algorithms and online algorithms for a number of scheduling and labeling (coloring) problems. Our work in the first part of the thesis is devoted to scheduling problems with the average weighted completion time objective function, that is primarily motivated by some theoretical questions which were open for a number of recent years. Here we present a general method which leads to the design of polynomial time approximation schemes (PTASs), best possible approximation results. In contrast, our work in the second part of the thesis is motivated by practical applications. We consider a number of new labeling and scheduling problems which occur in the design of communication networks. Here we present and analyze efficient approximation and online algorithms. We use very simple techniques which do not require large computational resources.