Constructing Self-non-intersecting OE-chains in a Plane Eulerian Graph

doi:10.14529/cmse190403

Efficient Algorithms for Max-Weighted Point Sweep Coverage on Lines

Sensors ◽

10.3390/s21041457 ◽

2021 ◽

Vol 21 (4) ◽

pp. 1457

Author(s):

Dieyan Liang ◽

Hong Shen

Keyword(s):

Optimal Algorithm ◽

Approximate Solutions ◽

Approximation Ratio ◽

Mobile Sensors ◽

Np Hard ◽

Coverage Problem ◽

Polynomial Time Approximation Algorithm ◽

Weighted Point ◽

Eulerian Graph ◽

Set Of Points

As an important application of wireless sensor networks (WSNs), deployment of mobile sensors to periodically monitor (sweep cover) a set of points of interest (PoIs) arises in various applications, such as environmental monitoring and data collection. For a set of PoIs in an Eulerian graph, the point sweep coverage problem of deploying the fewest sensors to periodically cover a set of PoIs is known to be Non-deterministic Polynomial Hard (NP-hard), even if all sensors have the same velocity. In this paper, we consider the problem of finding the set of PoIs on a line periodically covered by a given set of mobile sensors that has the maximum sum of weight. The problem is first proven NP-hard when sensors are with different velocities in this paper. Optimal and approximate solutions are also presented for sensors with the same and different velocities, respectively. For M sensors and N PoIs, the optimal algorithm for the case when sensors are with the same velocity runs in O(MN) time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio 12; for the general case of arbitrary velocities, 12α and 12(1−1/e) approximation algorithms are presented, respectively, where integer α≥2 is the tradeoff factor between time complexity and approximation ratio.

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Incorporating Maintenance Infeasibilities in an Aircraft Rotation Planning Model

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595920500256 ◽

2021 ◽

pp. 2050025

Author(s):

Ram Gopalan

Keyword(s):

Computational Complexity ◽

Theoretical Analysis ◽

Development Process ◽

Planning Model ◽

Sufficient Time ◽

Fleet Assignment ◽

Routing Problem ◽

Eulerian Graph ◽

Maintenance Requirements ◽

Periodic Routing

In any airline’s schedule development process, aircraft rotations must be planned for individual fleet types after fleet assignment. The aircraft rotation plans must conform to stringent maintenance requirements and this problem can be formulated as a periodic routing problem on an Eulerian graph. We analyze the computational complexity of developing maintenance rotations when some overnighting aircraft may not have sufficient time on the ground to complete extended maintenance (referred to as a maintenance infeasibility). The paper also provides a theoretical analysis of heuristics for the aircraft maintenance rotation problem with maintenance infeasibilities.

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Subsemi-Eulerian graphs

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171282000520 ◽

1982 ◽

Vol 5 (3) ◽

pp. 553-564 ◽

Cited By ~ 2

Author(s):

Charles Suffel ◽

Ralph Tindell ◽

Cynthia Hoffman ◽

Manachem Mandell

Keyword(s):

Eulerian Graphs ◽

Related Notion ◽

Minimum Number ◽

Eulerian Graph

A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.In this paper, we consider the related notion of a subsemi-eulerian graph, i.e. a graph which is spanned by a supergraph having an open trail containing all of its lines. The subsemi-eulerian graphs are characterized and formulas for the minimum number of required additional lines are given. Interrelationships between the two problems are stressed as well.

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