When Trees Grow Low: Shrubs and Fast MSO1

• Název česky: Když stromy nízké: Keře a rychlá MSO1
• Autoři: GANIAN Robert; HLINĚNÝ Petr; OBDRŽÁLEK Jan; NEŠETŘIL Jaroslav; OSSONA DE MENDEZ Patrice; RAMADURAI Reshma
• Rok publikování: 2012
• Druh: Článek ve sborníku
• Konference: Math Foundations of Computer Science MFCS 2012
• Fakulta / Pracoviště MU: Fakulta informatiky
• Doi: http://dx.doi.org/10.1007/978-3-642-32589-2_38
• Obor: Informatika
• Klíčová slova: tree-depth; shrub-depth; MSO model checking
• Popis: Recent characterization [9] of those graphs for which coloured MSO2 model checking is fast raised the interest in the graph invariant called tree-depth. Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class. To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes the graph classes having interpretation in coloured trees of bounded height. We also introduce a common extension of cographs and of graphs with bounded shrub-depth - m-partite cographs (still of bounded clique-width), which are well quasi-ordered by the relation “is an induced subgraph of” and therefore allow polynomial time testing of hereditary properties.

Související projekty

• Rozsáhlé výpočetní systémy: modely, aplikace a verifikace
• Centrum excelence - Institut teoretické informatiky
• Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity