Packing Cubes into a Cube Is NP-Hard in the Strong Sense

2013 ◽  
pp. 603-613
Author(s):  
Yiping Lu ◽  
Danny Z. Chen ◽  
Jianzhong Cha
Keyword(s):  
Strong Sense ◽  
Np Hard

scholarly journals Channel Density Minimization by Pin Permutation

VLSI Design ◽  
1994 ◽  
Vol 2 (2) ◽  
pp. 171-183
Author(s):  
Yang Cai ◽  
D. F. Wong ◽  
Jason Cong
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Layout Design ◽  
Strong Sense ◽  
Np Hard ◽  
Wire Length ◽  
Channel Density ◽  
Time Optimal ◽  
Two Sides ◽  
Intergrated Circuits

We present in this paper a linear time optimal algorithm for minimizing the density of a channel (with exits) by permuting the terminals on the two sides of the channel. This compares favorably with the previously known near-optimal algorithm presented in [6] that runs in superlinear time. Our algorithm has important applications in hierarchical layout design of intergrated circuits. We also show that the problem of minimizing wire length by permuting terminals is NP-hard in the strong sense.

Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems

2014 ◽  
Vol 962-965 ◽  
pp. 2868-2871 ◽  
Author(s):  
Alexander V. Chekanin ◽  
Vladislav A. Chekanin
Keyword(s):  
Data Structure ◽  
Linked Data ◽  
Bin Packing ◽  
High Efficiency ◽  
Optimization Problems ◽  
Packing Problem ◽  
Strong Sense ◽  
Np Hard ◽  
Packing Problems ◽  
Orthogonal Packing Problem

The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.

Two-Machine Flowshop Problem with Release Dates, Rejection and Non-Availability Interval on the First Machine

2014 ◽  
Vol 620 ◽  
pp. 80-83 ◽  
Author(s):  
Xie Xie ◽  
Xiang Yu Kong ◽  
Yong Yue Zheng ◽  
Kun Wei
Keyword(s):  
Heuristic Method ◽  
Strong Sense ◽  
Release Dates ◽  
Np Hard ◽  
Worst Case ◽  
Maximal Profit ◽  
Rejection Penalty ◽  
Flowshop Problem

This paper studies a two-machine flowshop problem with release dates, rejection and non-availability interval on the first machine. The non-availability interval often origins from equipments maintain or man-power. Usually, in order to pursue maximal profit, some jobs which can be rejected, and in this situation the rejection penalty should be paid. Our objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. For this demonstrated NP-hard in strong sense, we propose a heuristic method and further demonstrate that its worst case performance is 3.

Development of the Multimethod Genetic Algorithm for the Strip Packing Problem

2014 ◽  
Vol 598 ◽  
pp. 377-381 ◽  
Author(s):  
Vladislav A. Chekanin ◽  
Alexander V. Chekanin
Keyword(s):  
Genetic Algorithm ◽  
Packing Problem ◽  
Strong Sense ◽  
Np Hard ◽  
Two Dimensional ◽  
Strip Packing ◽  
Packing Problems ◽  
Total Length

The actual in industry strip packing problem which is NP-hard in strong sense is considered in paper. To the strip packing problem comes down solution of a large number of different practical problems, including problems in logistics, scheduling and planning. The new heuristics intended to pack a given set of rectangular two-dimensional objects in order to minimize of the total length of the filled part of container with an infinity length and fixed width are offered. The proposed multimethod genetic algorithm is investigated on well-known standard benchmarks of two-dimensional strip packing problems.

scholarly journals Evolutionary solving of the debts’ clearing problem

2019 ◽  
Vol 11 (2) ◽  
pp. 142-158
Author(s):  
Csaba Păatcaş ◽  
Attila Bartha
Keyword(s):  
Artificial Intelligence ◽  
Evolutionary Algorithm ◽  
Strong Sense ◽  
Np Hard ◽  
Intractable Problems

Abstract The debts’ clearing problem is about clearing all the debts in a group of n entities (banks, companies etc.) using a minimal number of money transaction operations. The problem is known to be NP-hard in the strong sense. As for many intractable problems, techniques from the field of artificial intelligence are useful in finding solutions close to optimum for large inputs. An evolutionary algorithm for solving the debts’ clearing problem is proposed.

Improved Data Structure for the Orthogonal Packing Problem

2014 ◽  
Vol 945-949 ◽  
pp. 3143-3146 ◽  
Author(s):  
Vladislav A. Chekanin ◽  
Alexander V. Chekanin
Keyword(s):  
Data Structure ◽  
Linked Data ◽  
Packing Problem ◽  
High Time ◽  
Strong Sense ◽  
Computational Experiments ◽  
Np Hard ◽  
Time Efficiency ◽  
Linked List ◽  
Orthogonal Packing Problem

In paper is considered the actual in industry and engineering orthogonal multidimensional packing problem. This problem is NP-hard in strong sense therefore an important role is played effectiveness of the used packing representation model. To increase the speed of placement of a given set of orthogonal objects into containers is offered a new data structure – multilevel linked data structure. The carried out computational experiments demonstrate high time efficiency of the proposed data structure compared to the ordered simple linked list.

Welsh Politics after the EU Referendum

2017 ◽  
Vol 26 (2) ◽  
pp. 212-228 ◽  
Author(s):  
John Osmond
Keyword(s):  
Effective Leadership ◽  
Strong Sense ◽  
Speaking Up ◽  
Common Cause ◽  
National Assembly ◽  
Working Together ◽  
Eu Referendum ◽  
Welsh Politics ◽  
Plaid Cymru ◽  
The Eu

This paper examines the electoral and ideological contest that has taken place between Welsh Labour and Plaid Cymru in the five National Assembly elections that have been held between 1999 and 2016. Both parties have found success when they have managed to combine effective leadership with a coherent programme and a strong sense of Welsh identity. However, the Welsh vote to leave the EU in the June 2016 referendum has dealt both parties a poor hand in speaking up for Welsh interests. Can they find a common cause in working together and also with Scotland to take Wales forward in a progressive constitutional direction?

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

Why Does Rationality Matter?

2017 ◽  
Author(s):  
Ralph Wedgwood
Keyword(s):  
Mental States ◽  
External World ◽  
Dutch Book ◽  
Strong Sense ◽  
General Characterization ◽  
Internal Rationality

Internalism implies that rationality requires nothing more than what in the broadest sense counts as ‘coherence’. The earlier chapters of this book argue that rationality is in a strong sense normative. But why does coherence matter? The interpretation of this question is clarified. An answer to the question would involve a general characterization of rationality that makes it intuitively less puzzling why rationality is in this strong sense normative. Various approaches to this question are explored: a deflationary approach, the appeal to ‘Dutch book’ theorems, the idea that rationality is constitutive of the nature of mental states. It is argued that none of these approaches solves the problem. An adequate solution will have to appeal to some value that depends partly on how things are in the external world—in effect, an external goal—and some normatively significant connection between internal rationality and this external goal.

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