The maximum weight hierarchy matching problem

2009 ◽  
Vol 10 (2) ◽  
pp. 198-206 ◽  
Author(s):  
Ron Zohar ◽  
Reuven Bar Yehuda
Keyword(s):  
Maximum Weight ◽  
Matching Problem ◽  
Weight Hierarchy

scholarly journals The Maximum-Weight Stable Matching Problem: Duality and Efficiency

2012 ◽  
Vol 26 (3) ◽  
pp. 1346-1360 ◽  
Author(s):  
Xujin Chen ◽  
Guoli Ding ◽  
Xiaodong Hu ◽  
Wenan Zang
Keyword(s):  
Stable Matching ◽  
Maximum Weight ◽  
Matching Problem

scholarly journals An O(n^3) time algorithm for the maximum weight b-matching problem on bipartite graphs

2020 ◽  
Author(s):  
Fatemeh Rajabi-Alni ◽  
Alireza Bagheri ◽  
Behrouz Minaei-Bidgoli
Keyword(s):  
Computational Biology ◽  
Bipartite Graph ◽  
Association Studies ◽  
Time Algorithm ◽  
Bipartite Graphs ◽  
Maximum Weight ◽  
Positive Real ◽  
Matching Problem ◽  
Genome Wide ◽  
Integer Weight

Abstract Background: A matching between two sets A and B assigns some elements of A to some elements of B. Finding the similarity between two sets of elements by advantage of the matching is widely used in computational biology for example in the contexts of genome-wide and sequencing association studies. Frequently, the capacities of the elements are limited. That is, the number of the elements that can be matched to each element should not exceed a given number. Results: We use bipartite graphs to model relationships between pairs of objects. Given an undirected bipartite graph G = (A [ B;E), the b-matching of G matches each vertex v in A (resp. B) to at least 1 and at most b(v) vertices in B (resp. A), where b(v) denotes the capacity of v. We propose the rst O(n3) time algorithm for nding the maximum weight b-matching of G, where jAj + jBj = O(n). Conclusions: The b-matching has been studied widely for the bipartite graphs with integer weight edges. But our algorithm is the rst algorithm for the maximum (respectively minimum) b-matching problem with non positive real (respectively non negative real) edge weights.

scholarly journals An O(n3) time algorithm for the maximum weight b-matching problem on bipartite graphs

2020 ◽  
Author(s):  
Fatemeh Rajabi-Alni ◽  
Alireza Bagheri ◽  
Behrouz Minaei-Bidgoli
Keyword(s):  
Computational Biology ◽  
Bipartite Graph ◽  
Association Studies ◽  
Time Algorithm ◽  
Bipartite Graphs ◽  
Maximum Weight ◽  
Positive Real ◽  
Matching Problem ◽  
Genome Wide ◽  
Integer Weight

Abstract Background: A matching between two sets A and B assigns some elements of A to some elements of B. Finding the similarity between two sets of elements by advantage of the matching is widely used in computational biology for example in the contexts of genome-wide and sequencing association studies. Frequently, the capacities of the elements are limited. That is, the number of the elements that can be matched to each element should not exceed a given number. Results: We use bipartite graphs to model relationships between pairs of objects. Given an undirected bipartite graph G = (A∪B,E), the b-matching of G matches each vertex v in A (resp. B) to at least 1 and at most b(v) vertices in B (resp. A), where b(v) denotes the capacity of v. We propose the first O(n3) time algorithm for finding the maximum weight b-matching of G, where |A|+|B| = O(n). Conclusions: The b-matching has been studied widely for the bipartite graphs with integer weight edges. But our algorithm is the first algorithm for the maximum (respectively minimum) b-matching problem with non positive real (respectively non negative real) edge weights.

Online Dynamic B-Matching

2021 ◽  
Vol 48 (3) ◽  
pp. 99-108
Author(s):  
Marcin Bienkowski ◽  
David Fuchssteiner ◽  
Jan Marcinkowski ◽  
Stefan Schmid
Keyword(s):  
Network Performance ◽  
Online Algorithm ◽  
Temporal Structure ◽  
Algorithmic Problem ◽  
Maximum Weight ◽  
Matching Problem ◽  
Asymptotically Optimal ◽  
Datacenter Networks ◽  
Maximum Weight Matching ◽  
Theoretical Results

This paper initiates the study of online algorithms for the maximum weight b-matching problem, a generalization of maximum weight matching where each node has at most b≥1 adjacent matching edges. The problem is motivated by emerging optical technologies which allow to enhance datacenter networks with reconfigurable matchings, providing direct connectivity between frequently communicating racks. These additional links may improve network performance, by leveraging spatial and temporal structure in the workload. We show that the underlying algorithmic problem features an intriguing connection to online paging (a.k.a. caching), but introduces a novel challenge. Our main contribution is an online algorithm which is O(b)- competitive; we also prove that this is asymptotically optimal. We complement our theoretical results with extensive trace-driven simulations, based on real-world datacenter workloads as well as synthetic traffic traces.

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.

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