TY - GEN
T1 - Dynamic programming approach to the generalized minimum manhattan network problem
AU - Masumura, Yuya
AU - Oki, Taihei
AU - Yamaguchi, Yutaro
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2020.
PY - 2020
Y1 - 2020
N2 - We study the generalized minimum Manhattan network (GMMN) problem: given a set $$P$$ of pairs of points in the Euclidean plane $$\mathbb R^2$$, we are required to find a minimum-length geometric network which consists of axis-aligned segments and contains a shortest path in the $$L:1$$ metric (a so-called Manhattan path) for each pair in $$P$$. This problem commonly generalizes several NP-hard network design problems that admit constant-factor approximation algorithms, such as the rectilinear Steiner arborescence (RSA) problem, and it is open whether so does the GMMN problem. As a bottom-up exploration, Schnizler (2015) focused on the intersection graphs of the rectangles defined by the pairs in $$P$$, and gave a polynomial-time dynamic programming algorithm for the GMMN problem whose input is restricted so that both the treewidth and the maximum degree of its intersection graph are bounded by constants. In this paper, as the first attempt to remove the degree bound, we provide a polynomial-time algorithm for the star case, and extend it to the general tree case based on an improved dynamic programming approach.
AB - We study the generalized minimum Manhattan network (GMMN) problem: given a set $$P$$ of pairs of points in the Euclidean plane $$\mathbb R^2$$, we are required to find a minimum-length geometric network which consists of axis-aligned segments and contains a shortest path in the $$L:1$$ metric (a so-called Manhattan path) for each pair in $$P$$. This problem commonly generalizes several NP-hard network design problems that admit constant-factor approximation algorithms, such as the rectilinear Steiner arborescence (RSA) problem, and it is open whether so does the GMMN problem. As a bottom-up exploration, Schnizler (2015) focused on the intersection graphs of the rectangles defined by the pairs in $$P$$, and gave a polynomial-time dynamic programming algorithm for the GMMN problem whose input is restricted so that both the treewidth and the maximum degree of its intersection graph are bounded by constants. In this paper, as the first attempt to remove the degree bound, we provide a polynomial-time algorithm for the star case, and extend it to the general tree case based on an improved dynamic programming approach.
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U2 - 10.1007/978-3-030-53262-8_20
DO - 10.1007/978-3-030-53262-8_20
M3 - Conference contribution
AN - SCOPUS:85089233169
SN - 9783030532611
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 237
EP - 248
BT - Combinatorial Optimization - 6th International Symposium, ISCO 2020, Revised Selected Papers
A2 - Baïou, Mourad
A2 - Gendron, Bernard
A2 - Günlük, Oktay
A2 - Mahjoub, A. Ridha
PB - Springer
T2 - 6th International Symposium on Combinatorial Optimization, ISCO 2020
Y2 - 4 May 2020 through 6 May 2020
ER -