TY - GEN

T1 - On the minimum caterpillar problem in digraphs

AU - Okada, Taku

AU - Suzuki, Akira

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
This work is partially supported by JSPS Grant-in-Aid for Scientific Research, Grant Numbers 24.3660(A. Suzuki), 22700001(T. Ito) and 23500001(X. Zhou).

PY - 2013

Y1 - 2013

N2 - Suppose that each arc in a digraph D = (V, A) has two costs of non-negative integers, called a spine cost and a leaf cost. A caterpillar is a directed tree consisting of a single directed path (of spine arcs) and leaf vertices each of which is incident to the directed path by exactly one incoming arc (leaf arc). For a given terminal set K âŠ† V, we study the problem of finding a caterpillar in D such that it contains all terminals in K and its total cost is minimized, where the cost of each arc in the caterpillar depends on whether it is used as a spine arc or a leaf arc. In this paper, we first study the complexity status of the problem with respect to the number of terminals: the problem is solvable in polynomial time for any digraph with two terminals, while it is NP-hard for three terminals. We then give a linear-time algorithm to solve the problem for digraphs with bounded treewidth, where the treewidth for a digraph D is defined as the one for the underlying graph of D. Our algorithm runs in linear time even if |K| = O(|V|).

AB - Suppose that each arc in a digraph D = (V, A) has two costs of non-negative integers, called a spine cost and a leaf cost. A caterpillar is a directed tree consisting of a single directed path (of spine arcs) and leaf vertices each of which is incident to the directed path by exactly one incoming arc (leaf arc). For a given terminal set K âŠ† V, we study the problem of finding a caterpillar in D such that it contains all terminals in K and its total cost is minimized, where the cost of each arc in the caterpillar depends on whether it is used as a spine arc or a leaf arc. In this paper, we first study the complexity status of the problem with respect to the number of terminals: the problem is solvable in polynomial time for any digraph with two terminals, while it is NP-hard for three terminals. We then give a linear-time algorithm to solve the problem for digraphs with bounded treewidth, where the treewidth for a digraph D is defined as the one for the underlying graph of D. Our algorithm runs in linear time even if |K| = O(|V|).

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U2 - 10.1007/978-3-642-38768-5_66

DO - 10.1007/978-3-642-38768-5_66

M3 - Conference contribution

AN - SCOPUS:84884913241

SN - 9783642387678

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

SP - 729

EP - 736

BT - Computing and Combinatorics - 19th International Conference, COCOON 2013, Proceedings

T2 - 19th International Computing and Combinatorics Conference, COCOON 2013

Y2 - 21 June 2013 through 21 June 2013

ER -