Minimum Weighted Coloring of Triangulated Graphs, with Application to Maximum Weight Vertex Packing and Clique Finding in Arbitrary Graphs

1991 ◽  
Vol 20 (2) ◽  
pp. 209-221 ◽  
Author(s):  
Egon Balas ◽  
Jue Xue
Keyword(s):  
Maximum Weight ◽  
Vertex Packing ◽  
Triangulated Graphs ◽  
Arbitrary Graphs

Yield and seed productivity of pear rootstock forms in the conditions of the steppe zone of the Southern Urals

2020 ◽  
Vol 62 ◽  
pp. 39-47
Author(s):  
A. I. Lokhova ◽  
E. Z. Savin ◽  
A. M. Rusanov ◽  
A. A. Mushinskiy
Keyword(s):  
Steppe Zone ◽  
Southern Urals ◽  
Botanical Garden ◽  
Climatic Conditions ◽  
High Yield ◽  
State University ◽  
Maximum Weight ◽  
Seed Productivity ◽  
The Southern Urals ◽  
Typical Soil

The article presents the results of studying the diversity of pear rootstock forms in terms of yield and seed productivity. The research was carried out at the experimental sites of the Orenburg Experimental Station of Horticulture and Viticulture of AllRussian Horticultural Institute for Breeding, Agrotechnology and Nursery and the Botanical Garden of the Orenburg State University in 2017-2019, in typical soil and climatic conditions of the Orenburg city. The purpose of the study is to identify pear rootstock forms characterized by high yield and stable seed productivity for use in the future as a seed rootstock. During the research, 15 pear accessions were studied; the planting scheme was 6x4 m. As a result of research, it was found that the rootstock form Temno-zelenaya is characterized by a high yield (40 kg/tree). High seed productivity of more than 6 seeds in one fruit was observed in samples: Vernaya (6.0-6.5 pcs.), SK-1, SK-3 (6.1-7.8 pcs.), SK-2 (7.0-7.5 pcs.), Chang Bai Li (7.4-7.7 pcs.), Semennaya 214 (7.5-7.8 pcs.). It was revealed that the Xiao he Bai Li variety is characterized by the maximum weight of 1000 seeds (65.2 g). Analysis of accessions by seed yield established that a consistently high yield is observed in the varieties Chang Bai Li (2.5-4.2 %), Vernaya (3.96-4.18 %) and forms SK-1 (2.0-3.25%), SK-2 (2.25-2.75 %), SK-3 (1.43-4.0 %). Pear rootstock forms Chang Bai Li, Vernaya, Semennaya 214, SK-1, SK-2, SK-3 were identifi ed, which can be recommended for production testing as seed pear rootstocks for the conditions of the steppe zone of the Southern Urals.

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Improving the Smoothed Complexity of FLIP for Max Cut Problems

2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran
Keyword(s):  
General Framework ◽  
Edge Weight ◽  
Complete Graphs ◽  
Worst Case ◽  
Weight Density ◽  
Complete Problems ◽  
Substantial Progress ◽  
Run Time ◽  
Optimum Solution ◽  
Arbitrary Graphs

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .

scholarly journals Validation of Automated Chromosome Recovery in the Reconstruction of Ancestral Gene Order

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 160
Author(s):  
Qiaoji Xu ◽  
Lingling Jin ◽  
James H. Leebens-Mack ◽  
David Sankoff
Keyword(s):  
Phylogenetic Tree ◽  
Gene Order ◽  
Evolutionary Process ◽  
Gene Content ◽  
Ancestral Genome ◽  
Maximum Weight ◽  
Ancestral Gene ◽  
Maximum Weight Matching

The RACCROCHE pipeline reconstructs ancestral gene orders and chromosomal contents of the ancestral genomes at all internal vertices of a phylogenetic tree. The strategy is to accumulate a very large number of generalized adjacencies, phylogenetically justified for each ancestor, to produce long ancestral contigs through maximum weight matching. It constructs chromosomes by counting the frequencies of ancestral contig co-occurrences on the extant genomes, clustering these for each ancestor and ordering them. The main objective of this paper is to closely simulate the evolutionary process giving rise to the gene content and order of a set of extant genomes (six distantly related monocots), and to assess to what extent an updated version of RACCROCHE can recover the artificial ancestral genome at the root of the phylogenetic tree relating to the simulated genomes.

Three-dimensional asymmetric maximum weight lifting prediction considering dynamic joint strength

2021 ◽  
pp. 095441192098703
Author(s):  
Rahid Zaman ◽  
Yujiang Xiang ◽  
Jazmin Cruz ◽  
James Yang
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Three Dimensional ◽  
Optimization Method ◽  
Weight Lifting ◽  
Joint Torque ◽  
Maximum Weight ◽  
Angular Velocities ◽  
Asymmetric Lifting

In this study, the three-dimensional (3D) asymmetric maximum weight lifting is predicted using an inverse-dynamics-based optimization method considering dynamic joint torque limits. The dynamic joint torque limits are functions of joint angles and angular velocities, and imposed on the hip, knee, ankle, wrist, elbow, shoulder, and lumbar spine joints. The 3D model has 40 degrees of freedom (DOFs) including 34 physical revolute joints and 6 global joints. A multi-objective optimization (MOO) problem is solved by simultaneously maximizing box weight and minimizing the sum of joint torque squares. A total of 12 male subjects were recruited to conduct maximum weight box lifting using squat-lifting strategy. Finally, the predicted lifting motion, ground reaction forces, and maximum lifting weight are validated with the experimental data. The prediction results agree well with the experimental data and the model’s predictive capability is demonstrated. This is the first study that uses MOO to predict maximum lifting weight and 3D asymmetric lifting motion while considering dynamic joint torque limits. The proposed method has the potential to prevent individuals’ risk of injury for lifting.

Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach

2019 ◽  
Vol 18 (02) ◽  
pp. 445-463 ◽  
Author(s):  
Klaus D. Goepel
Keyword(s):  
Analytical Hierarchy Process ◽  
Analytic Functions ◽  
Decision Problem ◽  
Decision Criteria ◽  
Maximum Weight ◽  
Analytic Hierarchy ◽  
New Approach ◽  
Scale Functions ◽  
Decision Method ◽  
Hierarchy Process

The analytic hierarchy process (AHP) remains a popular multi-criteria decision method. One topic under discussion of AHP is the use of different scales to translate judgments into ratios. The author makes a new approach to compare different scale functions and to derive a recommendation for the application of scales. The approach is based on simple analytic functions and takes into consideration the number of criteria of the decision problem. A generalization of the so-called balanced scale is proposed, and a new adaptive-balanced scale is introduced. Scales are then categorized and compared based on weight boundaries and weight ratios, weight uncertainties, weight dispersion and number of decision criteria. Finally, a practical example of a decision hierarchy is presented applying the different scales. The results show that the generalized balanced scale improves weight dispersion and weight uncertainty in comparison to the fundamental AHP scale. The proposed adaptive-balanced scale overcomes the problem of a change of the maximum weight depending on the number of decision criteria.

scholarly journals A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes
Keyword(s):  
Fundamental Group ◽  
Infinite Graphs ◽  
Graphs Of Groups ◽  
Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

Design Criteria for Safer Manual Lifting by Men and Women

1982 ◽  
Vol 26 (6) ◽  
pp. 503-507
Author(s):  
Dudley G. Letbetter
Keyword(s):  
Muscle Fatigue ◽  
Material Handling ◽  
Human Anatomy ◽  
Design Criteria ◽  
Maximum Weight ◽  
Manual Lifting ◽  
Men And Women ◽  
Simple Graphs ◽  
Cardiovascular Capacity ◽  
Specific Material

Simplified design criteria are provided for two-handed, manual lifting by standing men and women, without selective assignment of personnel to specific material handling tasks. Based on a 1981 NIOSH report, application of these criteria requires no knowledge of human anatomy, anthropometry, biomechanics, psychophysics, muscle fatigue, cardiovascular capacity, or metabolic endurance. A person who can read and use simple graphs can quickly determine the maximum weight of a lifted object. The information needed is the horizontal grasp distance and the initial grasp height and lift distance of the object, plus the frequency and duration of lifting.

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