Applications of a special polynomial class of TSP

A hypothetical problem which we call a "buried treasure problem" is presented where the objective is to locate m objects among N fixed equi-spaced caches in order to minimize a measure of the risk of loss. The general problem is shown to be NP-hard. However, a sub problem may be solved as a special class of TSP in O (N log N) time. Several applications are noted.

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Optimal Order Picking in Carousels Storage System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.601.347 ◽

2012 ◽

Vol 601 ◽

pp. 347-353

Author(s):

Xiong Zhi Wang ◽

Guo Qing Wang

Keyword(s):

Approximation Algorithm ◽

General Problem ◽

Storage System ◽

Order Picking ◽

Total Order ◽

Experimental Results ◽

Optimal Order ◽

Np Hard ◽

Special Case

We study the order picking problem in carousels system with a single picker. The objective is to find a picking scheduling to minimizing the total order picking time. After showing the problem being strongly in NP-Hard and finding two characteristics, we construct an approximation algorithm for a special case (two carousels) and a heuristics for the general problem. Experimental results verify that the solutions are quickly and steadily achieved and show its better performance.

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PEMBINAAN SISWA BERBAKAT DAN BERPRESTASI DI SMA NEGERI 1 SEMARANG

Jurnal VARIDIKA ◽

10.23917/varidika.v24i2.709 ◽

2015 ◽

Vol 24 (2) ◽

Author(s):

Esti Gusti Arini

Keyword(s):

High School ◽

Data Analysis ◽

General Problem ◽

Special Class ◽

Learning Experience ◽

Senior High School ◽

Learning Activity ◽

Talented Student ◽

Model Study ◽

Strategy Construction

Talented student is student who owns ability more than a student in general. Problem which often happens at school in Indonesia is minim of education to talented student. In accommodating fund channel potency to talented student, State Senior High School 1 of Semarang forms special class to talented student and has achievement. Based on background, this research aims to 1) to descripbe strategy construction of student in State Senior High School 1 of Semarang and to descripbe execution of construction of student in State Senior High School 1 of Semarang. This type of research is qualitative ethnography. This research is executed in State Senior High School 1 of Semarang. Subject research is the principal, teacher, and student. Method data collecting use circumstantial interview, observation, and documentation. Data analysis in this research is ethnography analysis. Test authenticity of data by test credibility, transformabilitiy, and conformabilities of expendabilities. The results are 1) Strategy construction of student based on achievement and talent in State Senior High School 1 of Semarang is model study of subdividing of talented student in class of especially with pleasant study strategy and in construction of talented student and have achievement needed and 2) execution of construction of student based on achievement and talent in State Senior High School 1 of Semarang passes some developments with instruction strategy. Those are, first, study bases on problem. Second is exploiting student environment to obtain learning experience. Thirdly, is group activity. Fourth, is making autodidact activity. Fifth is making learning activity to cooperate with society. Sixth is applying assessment of authentic

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Topology and growth of a special class of holomorphic self-maps of ℂ*

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700004995 ◽

1989 ◽

Vol 9 (2) ◽

pp. 321-328 ◽

Cited By ~ 2

Author(s):

Linda Keen

Keyword(s):

Dynamical Systems ◽

General Problem ◽

Moduli Spaces ◽

Special Class ◽

The Family ◽

Image Position

AbstractIt is a general problem to find appropriate sets of moduli for families of functions that generate dynamical systems. In this paper we solve this problem for a specific family of holomorphic self-maps of ℂ* defined byThe main theorem states that any function topologically conjugate to a member of ℱ is holomorphically conjugate to some member of the family. It follows that the coefficients of the polynomials P(z) and Q(z) are a suitable set of moduli for the families of dynamical systems generated by these functions.The moduli spaces of functions in ℱ are easy to study computationally and have been studied by many authors. (See references in the text.)

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On Finding and Enumerating Maximal and Maximum k-Partite Cliques in k-Partite Graphs

Algorithms ◽

10.3390/a12010023 ◽

2019 ◽

Vol 12 (1) ◽

pp. 23 ◽

Cited By ~ 1

Author(s):

Charles Phillips ◽

Kai Wang ◽

Erich Baker ◽

Jason Bubier ◽

Elissa Chesler ◽

...

Keyword(s):

Functional Genomics ◽

Polynomial Time ◽

Special Class ◽

Bipartite Graphs ◽

Time Transformation ◽

Np Hard ◽

Maximum Element ◽

Heuristic Approaches ◽

Upper Limit ◽

Open Questions

Let k denote an integer greater than 2, let G denote a k-partite graph, and let S denote the set of all maximal k-partite cliques in G. Several open questions concerning the computation of S are resolved. A straightforward and highly-scalable modification to the classic recursive backtracking approach of Bron and Kerbosch is first described and shown to run in O(3n/3) time. A series of novel graph constructions is then used to prove that this bound is best possible in the sense that it matches an asymptotically tight upper limit on |S|. The task of identifying a vertex-maximum element of S is also considered and, in contrast with the k = 2 case, shown to be NP-hard for every k ≥ 3. A special class of k-partite graphs that arises in the context of functional genomics and other problem domains is studied as well and shown to be more readily solvable via a polynomial-time transformation to bipartite graphs. Applications, limitations, potentials for faster methods, heuristic approaches, and alternate formulations are also addressed.

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Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.1515/bpasts-2017-0004 ◽

2017 ◽

Vol 65 (1) ◽

pp. 29-34 ◽

Cited By ~ 1

Author(s):

H. Furmańczyk ◽

M. Kubale

Keyword(s):

Approximation Algorithm ◽

General Problem ◽

Unit Length ◽

Mutual Exclusion ◽

Np Hard ◽

Uniform Machines ◽

Identical Jobs ◽

Incompatibility Graph

Abstract In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 ≥ s2 ≥ s3 ≥ s4, respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree Δ, where two incompatible jobs cannot be processed on the same machine. We show that the general problem is NP-hard even if s1 = s2 = s3. If, however, Δ ≤ 4 and s1 ≥ 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n1.5). The same algorithm returns a solution of value at most 2 times optimal provided that s1 ≥ 2s2. Finally, we study the case s1 ≥ s2 ≥ s3 = s4 and give a 32/15-approximation algorithm running also in O(n1.5) time.

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Defending with Shared Resources on a Network

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i02.5585 ◽

2020 ◽

Vol 34 (02) ◽

pp. 2111-2118

Author(s):

Minming Li ◽

Long Tran-Thanh ◽

Xiaowei Wu

Keyword(s):

Lower Bound ◽

Approximation Algorithm ◽

Polynomial Time ◽

General Problem ◽

Exact Algorithm ◽

Exact Algorithms ◽

Np Hard ◽

Shared Resources ◽

Target Node ◽

Special Cases

In this paper we consider a defending problem on a network. In the model, the defender holds a total defending resource of R, which can be distributed to the nodes of the network. The defending resource allocated to a node can be shared by its neighbors. There is a weight associated with every edge that represents the efficiency defending resources are shared between neighboring nodes. We consider the setting when each attack can affect not only the target node, but its neighbors as well. Assuming that nodes in the network have different treasures to defend and different defending requirements, the defender aims at allocating the defending resource to the nodes to minimize the loss due to attack. We give polynomial time exact algorithms for two important special cases of the network defending problem. For the case when an attack can only affect the target node, we present an LP-based exact algorithm. For the case when defending resources cannot be shared, we present a max-flow-based exact algorithm. We show that the general problem is NP-hard, and we give a 2-approximation algorithm based on LP-rounding. Moreover, by giving a matching lower bound of 2 on the integrality gap on the LP relaxation, we show that our rounding is tight.

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Influence of Magnetic Fields on Solar Hydrodynamics: Experimental Results

International Astronomical Union Colloquium ◽

10.1017/s025292110005329x ◽

1977 ◽

Vol 36 ◽

pp. 143-180 ◽

Cited By ~ 10

Author(s):

J.O. Stenflo

Keyword(s):

Solar Activity ◽

Energy Balance ◽

Magnetic Fields ◽

Solar Atmosphere ◽

General Problem ◽

Solar Rotation ◽

Active Regions ◽

Physical Conditions ◽

Dynamic Phenomena

It is well-known that solar activity is basically caused by the Interaction of magnetic fields with convection and solar rotation, resulting in a great variety of dynamic phenomena, like flares, surges, sunspots, prominences, etc. Many conferences have been devoted to solar activity, including the role of magnetic fields. Similar attention has not been paid to the role of magnetic fields for the overall dynamics and energy balance of the solar atmosphere, related to the general problem of chromospheric and coronal heating. To penetrate this problem we have to focus our attention more on the physical conditions in the ‘quiet’ regions than on the conspicuous phenomena in active regions.

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