scholarly journals Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem

2006 ◽  
Vol 154 (16) ◽  
pp. 2402-2410 ◽  
Author(s):  
Keizo Miyata ◽  
Shigeru Masuyama ◽  
Shin-ichi Nakayama ◽  
Liang Zhao
Keyword(s):  
Approximation Algorithm ◽  
Spanning Tree ◽  
Vertex Ranking ◽  
Np Hardness

scholarly journals Transportation and Batching Scheduling for Minimizing Total Weighted Completion Time

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 819 ◽  
Author(s):  
Hongjun Wei ◽  
Jinjiang Yuan ◽  
Yuan Gao
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Completion Time ◽  
Total Weighted Completion Time ◽  
Single Vehicle ◽  
Weighted Completion Time ◽  
Np Hardness

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

SEPARATING POINTS BY AXIS-PARALLEL LINES

2005 ◽  
Vol 15 (06) ◽  
pp. 575-590 ◽  
Author(s):  
GRUIA CĂLINESCU ◽  
ADRIAN DUMITRESCU ◽  
HOWARD KARLOFF ◽  
PENG-JUN WAN
Keyword(s):  
Approximation Algorithm ◽  
Separation Problem ◽  
Lp Rounding ◽  
Parallel Lines ◽  
Point Separation ◽  
Axis Parallel ◽  
Minimum Number ◽  
Np Hardness

We study the problem of separating n points in the plane, no two of which have the same x- or y-coordinate, using a minimum number of vertical and horizontal lines avoiding the points, so that each cell of the subdivision contains at most one point. Extending previous NP-hardness results due to Freimer et al. we prove that this problem and some variants of it are APX-hard. We give a 2-approximation algorithm for this problem, and a d-approximation algorithm for the d-dimensional variant, in which the points are to be separated using axis-parallel hyperplanes. To this end, we reduce the point separation problem to the rectangle stabbing problem studied by Gaur et al. Their approximation algorithm uses LP-rounding. We present an alternative LP-rounding procedure which also works for the rectangle stabbing problem. We show that the integrality ratio of the LP is exactly 2.

SUBTREE TRANSFER DISTANCE FOR DEGREE-D PHYLOGENIES

2004 ◽  
Vol 15 (06) ◽  
pp. 893-909 ◽  
Author(s):  
WING-KAI HON ◽  
TAK-WAH LAM ◽  
SIU-MING YIU ◽  
MING-YANG KAO ◽  
WING-KIN SUNG
Keyword(s):  
Approximation Algorithm ◽  
Distance Metric ◽  
Transfer Distance ◽  
Np Hardness

The subtree transfer (STT) distance is one of the distance metric for comparing phylogenies. Previous work on computing the STT distance considered degree-3 trees only. In this paper, we give an approximation algorithm for the STT distance for degree-d trees with arbitrary d and with generalized STT operations. Also, some NP-hardness results related to STT distance are presented.

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