TY - GEN
T1 - 0/1/all CSPs, half-integral A-path packing, and linear-time FPT algorithms
AU - Iwata, Yoichi
AU - Yamaguchi, Yutaro
AU - Yoshida, Yuichi
N1 - Funding Information:
ACKNOWLEDGMENT We would like to thank Yusuke Kobayashi for pointing out to us the simulation of two-fan constraints by permutation constraints. Yoichi Iwata is supported by JSPS KAKENHI Grant Number JP17K12643. YutaroYamaguchiis supported by JSPS KAKENHI Grant Number JP16H06931 and JST ACT-I Grant Number JPMJPR16UR. Yuichi Yoshida is supported by JST ERATO Grant Number JPMJER1305 and JSPS KAKENHI Grant Number JP17H04676.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/11/30
Y1 - 2018/11/30
N2 - A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes a large polynomial in the input size because we need to compute half-integral optimal LP solutions. In this paper, we address this issue by providing an O(km)-time algorithm for solving the LPs arising from various FPT problems, where k is the optimal value and m is the number of edges/constraints. Our algorithm is based on interesting connections among 0/1/all constraints, which has been studied in the field of constraints satisfaction, A-path packing, which has been studied in the field of combinatorial optimization, and the LPs used in FPT algorithms. With the aid of this algorithm, we obtain linear-time FPT algorithms for various problems. The obtained running time for each problem is linear in the input size and has the current smallest dependency on the parameter. Most importantly, instead of using problem-specific approaches, we obtain all of these results by a unified approach, i.e., the branch-and-bound framework combined with the efficient computation of half-integral LPs, which demonstrates its generality.
AB - A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes a large polynomial in the input size because we need to compute half-integral optimal LP solutions. In this paper, we address this issue by providing an O(km)-time algorithm for solving the LPs arising from various FPT problems, where k is the optimal value and m is the number of edges/constraints. Our algorithm is based on interesting connections among 0/1/all constraints, which has been studied in the field of constraints satisfaction, A-path packing, which has been studied in the field of combinatorial optimization, and the LPs used in FPT algorithms. With the aid of this algorithm, we obtain linear-time FPT algorithms for various problems. The obtained running time for each problem is linear in the input size and has the current smallest dependency on the parameter. Most importantly, instead of using problem-specific approaches, we obtain all of these results by a unified approach, i.e., the branch-and-bound framework combined with the efficient computation of half-integral LPs, which demonstrates its generality.
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U2 - 10.1109/FOCS.2018.00051
DO - 10.1109/FOCS.2018.00051
M3 - Conference contribution
AN - SCOPUS:85059817724
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 462
EP - 473
BT - Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
A2 - Thorup, Mikkel
PB - IEEE Computer Society
T2 - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Y2 - 7 October 2018 through 9 October 2018
ER -