Recent Advances in Algorithmic Combinatorics (Hb)

Combinatorics is one of the fastest growing elds of mathematics In large measure this is because many practical problems can be modeled and then e ciently solved using combinatorial theory This real world motivation for studying algorithmic combinatorics has led not only to the development of many software packages but also to some beautiful mathematics which has nodirectapplicationtoappliedproblems Inthisvolumewehighlightsome exciting recent developments in algorithmic combinatorics Most practical applications of algorithmic combinatorics would be possible without the use of the computer As computers become ever more powerful more and more applications become possible Computational biology is one example of a relatively new eld in which algorithmic c binatorics plays a key role The chapter by Sagot and Wakabayashi in this volumediscusseshowcombinatorialtoolscanbeusedtosearchforpatterns in DNA and protein sequences The information technology revolution has not only allowed for the r olution of practical problems using combinatorial techniques it has also been the source of many new combinatorial problems One example is dio channel assignment In this problem we have a number of transmitters each of which must handle a number of calls Each call must be assigned a frequency in such a way that interference is avoided thus calls handled by the same transmitter are assigned di erent frequencies as are calls handled by transmitters which are near each other The explosive growth in the use of the frequency spectrum due to e g mobile telephone networks has made it a very valuable resource Combinatorics is one of the fastest growing fields of mathematics One reason for this is because many practical problems can be modeled and then efficiently solved using combinator combinatorial theory This real world motivation for studying algorithmic combinatorics has led not only to the development of many software packages but also to some beautiful ma