TY - GEN

T1 - Graph inference from a walk for trees of bounded degree 3 is NP-complete

AU - Maruyama, Osamu

AU - Miyano, Satoru

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1995.

PY - 1995

Y1 - 1995

N2 - The graph inference from a walk for a class C of undirected edgecolored graphs is, given a string x of colors, finding the smallest graph G in C that allows a traverse of all edges in G whose sequence of edge-colors is x, called a walk for x. We prove that the graph inference from a walk for trees of bounded degree k is NP-complete for any k ≥ 3, while the problem for trees without any degree bound constraint is known to be solvable in O(n) time, where n is the length of the string. Furthermore, the problem for a special class of trees of bounded degree 3, called (1,1)-caterpillars, is shown to be NP-complete. This contrast with the case that the problem for linear chains is known to be solvable in O(nlog n) time since a (1,1)-caterpillar is obtained by attaching at most one hair of length one to each node of a linear chain. We also show the MAXSNP-hardness of these problems.

AB - The graph inference from a walk for a class C of undirected edgecolored graphs is, given a string x of colors, finding the smallest graph G in C that allows a traverse of all edges in G whose sequence of edge-colors is x, called a walk for x. We prove that the graph inference from a walk for trees of bounded degree k is NP-complete for any k ≥ 3, while the problem for trees without any degree bound constraint is known to be solvable in O(n) time, where n is the length of the string. Furthermore, the problem for a special class of trees of bounded degree 3, called (1,1)-caterpillars, is shown to be NP-complete. This contrast with the case that the problem for linear chains is known to be solvable in O(nlog n) time since a (1,1)-caterpillar is obtained by attaching at most one hair of length one to each node of a linear chain. We also show the MAXSNP-hardness of these problems.

UR - http://www.scopus.com/inward/record.url?scp=84947918349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947918349&partnerID=8YFLogxK

U2 - 10.1007/3-540-60246-1_132

DO - 10.1007/3-540-60246-1_132

M3 - Conference contribution

AN - SCOPUS:84947918349

SN - 3540602461

SN - 9783540602460

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 257

EP - 266

BT - Mathematical Foundations of Computer Science 1995 - 20th International Symposium, MFCS 1995, Proceedings

A2 - Wiedermann, Jiri

A2 - Hajek, Petr

PB - Springer Verlag

T2 - 20th International Symposium on Mathematical Foundations of Computer Science, MFCS 1995

Y2 - 28 August 1995 through 1 September 1995

ER -