TY - JOUR

T1 - Inferring a tree from walks

AU - Maruyama, Osamu

AU - Miyano, Satoru

N1 - Funding Information:
We would like to thank Ayumi Shinohara for a greata mount of helps and suggestions in attacking problems discussed in this paper. We are also grateful to all refereesf or useful comments.T his work is partly supportedb y Grant-in-Aid for Scientific Research on Priority Areas “Genome Informatics” from the Ministry of Education, Science and Culture, Japan. The first author’s research is partly supported by Grants-in-Aid for JSPS researchf ellows from the Ministry of Education, Science and Culture, Japan.

PY - 1996/7/15

Y1 - 1996/7/15

N2 - A walk on an undirected edge-colored graph G is a path containing all edges of G. The tree inference from a walk is, given a string x of colors, finding the smallest tree that realizes a walk whose sequence of edge-colors coincides with x. We prove that the problem is solvable in O(n) time, where n is the length of a given string. We furthermore consider the problem of inferring a tree from a finite number of partial walks, where a partial walk on G is a path in G. We show that the problem turns to be NP-complete even if the number of colors is restricted to 3. It is also shown that the problem of inferring a linear chain from partial walks is NP-complete, while the linear chain inference from a single walk is known to be solvable in polynomial time.

AB - A walk on an undirected edge-colored graph G is a path containing all edges of G. The tree inference from a walk is, given a string x of colors, finding the smallest tree that realizes a walk whose sequence of edge-colors coincides with x. We prove that the problem is solvable in O(n) time, where n is the length of a given string. We furthermore consider the problem of inferring a tree from a finite number of partial walks, where a partial walk on G is a path in G. We show that the problem turns to be NP-complete even if the number of colors is restricted to 3. It is also shown that the problem of inferring a linear chain from partial walks is NP-complete, while the linear chain inference from a single walk is known to be solvable in polynomial time.

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U2 - 10.1016/0304-3975(95)00156-5

DO - 10.1016/0304-3975(95)00156-5

M3 - Article

AN - SCOPUS:0030182823

SN - 0304-3975

VL - 161

SP - 289

EP - 300

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-2

ER -