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.
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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 -