Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration.

Download Full-text

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

POMICULTURE & SMALL FRUITS CULTURE IN RUSSIA ◽

10.31676/2073-4948-2020-62-39-47 ◽

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.

Download Full-text

A Browser for Directed Graphs

10.21236/ada173877 ◽

1984 ◽

Author(s):

Lawrence A. Rowe ◽

Michael Davis ◽

Eli Messinger ◽

Carl Meyer ◽

Charles Spirakis

Keyword(s):

Directed Graphs

Download Full-text

A Browser for Directed Graphs

10.21236/ada166622 ◽

1985 ◽

Author(s):

Carl Meyer

Keyword(s):

Directed Graphs

Download Full-text

Distributed empirical risk minimization over directed graphs

2019 53rd Asilomar Conference on Signals, Systems, and Computers ◽

10.1109/ieeeconf44664.2019.9049065 ◽

2019 ◽

Cited By ~ 1

Author(s):

Ran Xin ◽

Anit Kumar Sahu ◽

Soummya Kar ◽

Usman A. Khan

Keyword(s):

Directed Graphs ◽

Empirical Risk Minimization ◽

Risk Minimization ◽

Empirical Risk

Download Full-text

On the star forest polytope for trees and cycles

RAIRO - Operations Research ◽

10.1051/ro/2018076 ◽

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.

Download Full-text

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

Algorithms ◽

10.3390/a14060160 ◽

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.

Download Full-text