How to pack directed acyclic graphs into small blocks

Yuichi Asahiro, Tetsuya Furukawa, Keiichi Ikegami, Eiji Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


The paper studies the following variant of clustering or laying out problems of graphs: Given a directed acyclic graph (DAG for short), the objective is to find a mapping of its nodes into blocks of size at most B that minimizes the maximum number of external arcs during traversals of the acyclic structure by following paths from the roots to the leaves. An external arc is defined as an arc connecting two distinct blocks. The problem can be shown to be NP-hard generally, and to remain intractable even if B = 2 and the height of DAGs is three. In this paper we provide a 3/2 factor linear time approximation algorithm for B = 2, and prove that the 3/2 ratio is optimal in terms of approximation guarantee. In the case of B ≥ 3, we also show that there is no 3/2 - ε factor approximation algorithm assuming P ≠ NP, where ε is arbitrarily small positive. Furthermore, we give a 2 factor approximation algorithm for B = 3 if the input is restricted to a set of layered graphs.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 6th Italian Conference, CIAC 2006, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)354034375X, 9783540343752
Publication statusPublished - 2006
Event6th Italian Conference on Algorithms and Complexity, CIAC 2006 - Rome, Italy
Duration: May 29 2006May 31 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3998 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other6th Italian Conference on Algorithms and Complexity, CIAC 2006

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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