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Colorful Frontier-Based Search: Implicit Enumeration of Chordal and Interval Subgraphs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11544)


This paper considers enumeration of specific subgraphs of a given graph by using a data structure called a zero-suppressed binary decision diagram (ZDD). A ZDD can represent the set of solutions quite compactly. Recent studies have demonstrated that a technique generically called frontier-based search (FBS) is a powerful framework for using ZDDs to enumerate various yet rather simple types of subgraphs. We in this paper, propose colorful FBS, an enhancement of FBS, which enables us to enumerate more complex types of subgraphs than existing FBS techniques do. On the basis of colorful FBS, we design methods that construct ZDDs representing the sets of chordal and interval subgraphs from an input graph. Computer experiments show that the proposed methods run faster than reverse search based algorithms.


  • Graph algorithm
  • Graph enumeration
  • Decision diagram
  • Frontier-based search
  • Interval graph
  • Chordal graph

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This work was supported in part by JSPS KAKENHI Grant Numbers JP15H05711, JP18K04610, JP16K16006, JP18H04091 and JP19K12098, and NAIST Big Data Project.

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Correspondence to Jun Kawahara .

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Kawahara, J., Saitoh, T., Suzuki, H., Yoshinaka, R. (2019). Colorful Frontier-Based Search: Implicit Enumeration of Chordal and Interval Subgraphs. In: Kotsireas, I., Pardalos, P., Parsopoulos, K., Souravlias, D., Tsokas, A. (eds) Analysis of Experimental Algorithms. SEA 2019. Lecture Notes in Computer Science(), vol 11544. Springer, Cham.

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