Graph Separator Algorithms: A Refined Analysis

This paper continues our research on the use of graph separator theorems for designing fixed parameter algorithms started with the COCOON’01 contribution [2], showing how a more elaborated use of these theorems can bring down the algorithmically relevant constants. More precisely, if a cÖ</font >k c^{\sqrt k } -algorithm is obtainable with the help of applying the well-known Lipton/Tarjan planar separator theorem, our new approach will lead to a c2 \mathord/ \vphantom 2 3 3Ö</font >k c^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}\sqrt k } -algorithm, this way also improving on the direct use of the “best” known planar separator theorem. For several problems, the constants can be even improved more by analyzing other separator theorems.