Enumeration of Architectures With Perfect Matchings

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Daniel R. Herber ◽  
Tinghao Guo ◽  
James T. Allison

In this article, a class of architecture design problems is explored with perfect matchings (PMs). A perfect matching in a graph is a set of edges such that every vertex is present in exactly one edge. The perfect matching approach has many desirable properties such as complete design space coverage. Improving on the pure perfect matching approach, a tree search algorithm is developed that more efficiently covers the same design space. The effect of specific network structure constraints (NSCs) and colored graph isomorphisms on the desired design space is demonstrated. This is accomplished by determining all unique feasible graphs for a select number of architecture problems, explicitly demonstrating the specific challenges of architecture design. With this methodology, it is possible to enumerate all possible architectures for moderate scale-systems, providing both a viable solution technique for certain problems and a rich data set for the development of more capable generative methods and other design studies.

Author(s):  
Daniel R. Herber ◽  
Tinghao Guo ◽  
James T. Allison

In this article a class of architecture design problems is explored with perfect matchings. A perfect matching in a graph is a set of edges such that every vertex is present in exactly one edge. The perfect matching approach has many desirable properties such as complete design space coverage. Improving on the pure perfect matching approach, a tree search algorithm is developed that more efficiently covers the same design space. The effect of specific network structure constraints and colored graph isomorphisms on the desired design space is demonstrated. This is accomplished by determining all unique feasible graphs for a select number of architecture problems, explicitly demonstrating the specific challenges of architecture design. Additional applications of this work to the larger architecture design process is also discussed.


2010 ◽  
Vol 19 (5-6) ◽  
pp. 791-817 ◽  
Author(s):  
CATHERINE GREENHILL ◽  
SVANTE JANSON ◽  
ANDRZEJ RUCIŃSKI

Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint) and replacing each edge by a randomly chosen perfect matching between the n-sets corresponding to the endpoints of the edge. Let XG be the number of perfect matchings in a random lift of G. We study the distribution of XG in the limit as n tends to infinity, using the small subgraph conditioning method.We present several results including an asymptotic formula for the expectation of XG when G is d-regular, d ≥ 3. The interaction of perfect matchings with short cycles in random lifts of regular multigraphs is also analysed. Partial calculations are performed for the second moment of XG, with full details given for two example multigraphs, including the complete graph K4.To assist in our calculations we provide a theorem for estimating a summation over multiple dimensions using Laplace's method. This result is phrased as a summation over lattice points, and may prove useful in future applications.


2012 ◽  
Vol 72 (1) ◽  
pp. 134-167 ◽  
Author(s):  
SHEILAGH OGILVIE ◽  
MARKUS KÜPKER ◽  
JANINE MAEGRAITH

The “less-developed” interior of early modern Europe, especially the rural economy, is often regarded as financially comatose. This article investigates this view using a rich data set of marriage and death inventories for seventeenth-century Germany. It first analyzes the characteristics of debts, examining borrowing purposes, familial links, communal ties, and documentary instruments. It then explores how borrowing varied with gender, age, marital status, occupation, date, and asset portfolio. It finds that ordinary people, even in a “less-developed” economy in rural central Europe, sought to invest profitably, smooth consumption, bridge low liquidity, and hold savings in financial form.


2011 ◽  
Vol 374-377 ◽  
pp. 268-272
Author(s):  
Hai Yun Wang ◽  
Jing Shi

In this essay, the cooling method design was discussed from the perspective of architecture design using passive design based on the climate and geological environment of Shenzhen city. It concluded that shading and natural ventilation should be the major cooling method for this area, and design recommendations were put forward based on analysis from the perspective of plan layout, shape design, space form and detailed construction design.


2021 ◽  
Author(s):  
◽  
Ellen Yarrow

<p>This study explores the relationship between professional contractors and the permanent employees they work with at organisations in New Zealand. This thesis uses two concepts, organisational socialisation and the psychological contract, as lenses through which the working relationship is explored. The 20th century notion of standard employment has largely been eroded, giving way to different forms of non-standard work. Professional contractors are now found performing a variety of roles in many organisations across this country. Many are doing the work of permanent employees, but they are neither employees nor permanent. Professional contractors are a type of non-standard, transient worker. As part of a blended workforce, professional contractors work alongside permanent employees, but little is known about how they work together.  This qualitative study involves 49 face-to-face interviews with professional contractors, permanent employees and managers working in the Information Technology (IT) divisions of 10 organisations in three major cities in New Zealand. This research design results in a rich data set. The data collected was subject to analysis using the software NVIVO. This data was analysed in relation to the literature on organisational socialisation and the psychological contract to further explain the working relationship between professional contractors and permanent employees.  The findings reveal professional contractors’ experience of Van Maanen’s (1979) socialisation tactics were: collective, informal, variable, random and serial. It was found that an organisation’s policy sets the tone for the treatment (induction, inclusion and management) of professional contractors. According to the professional contractors interviewed, the Chao, O'Leary-Kelly, Wolf, Klein, and Gardner (1994) socialisation content dimensions that are important are structure, culture and values and language but history was not considered important. According to the managers interviewed, contractors need to know about the processes and procedures of the client organisation, have strong technical skills and industry, sector or domain knowledge. It was found that the indicator of adjustment ‘acceptance by insiders’ (Bauer & Erdogan, 2012) may be a sign that the contractor is adjusting to their new role but it is not essential. A new indicator of adjustment for professional contractors – output – clearly emerged from the data. The notion of ‘time to productivity’ is highly relevant to professional contractors and three factors affecting it are identified (contractor capability, role complexity and organisation readiness). Another important finding is that permanent employees play a key role as socialisation agents (Feldman, 1994; Jones, 1983; Van Maanen, 1978) in the socialisation of professional contractors. Surprisingly, it was found that other professional contractors also act as socialisation agents assisting the newcomer to adjust. It was found that proactive socialisation is particularly important for professional contractors. Together these findings establish the need to reconceptualise organisational socialisation for professional contractors specifically.  The second part of this thesis explores the psychological contract by asking interviewees about their mutual expectations. The expectations of each of the three parties (managers, professional contractors, and permanent employees) are subtly different, potentially influencing the psychological contract they develop. Permanent employees expect great things, professionalism and independence from professional contractors. Managers expect speed, professionalism and value for money from contractors. On the other hand, professional contractors simply expect to be treated with respect by their colleagues. Professional contractors expect to be given autonomy by their managers and support or guidance, should they require it. This study was not able to ascertain what type of psychological contract a professional contractor may develop. It is possible that a professional contractor develops a hybrid psychological contract. Alternatively, it is possible that a professional contractor’s psychological contract moves between the types developed by Rousseau (1995) over the course of their term with the client organisation. The insights gained by exploring the expectations of professional contractors, permanent employees and their managers are two-fold. Firstly, these expectations provide a valuable insight into the working relationship. Secondly, the exploration of a breach or violation of the psychological contract indicates that a malleable psychological contract (one that will shift or adjust) is less likely to manifest a breach or violation. Therefore, it is better for a professional contractor to develop and maintain a malleable rather than rigid psychological contract.  This study’s findings highlight the interrelationship between organisational socialisation and the psychological contract. This thesis asserts that the working relationship between professional contractors and permanent employees is specifically influenced by the socialisation of contractors as newcomers and in the mutual expectations, which form the psychological contract. As a result, it contributes to theorising and understanding of the working relationship between professional contractors and permanent employees. It identifies several tensions in the co-dependent working relationship, which are: time, team, treatment and training. This study has implications for Human Resource practitioners and managers because there is a need for corporate or HR policy relating to the treatment professional contractors. The use of organisational socialisation and the psychological contract as lenses with which the working relationship is explored is both original and meaningful.</p>


10.37236/3540 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Dong Ye ◽  
Heping Zhang

A graph $G$ with a perfect matching is Pfaffian if it admits an orientation $D$ such that every central cycle $C$ (i.e. $C$ is of even size and $G-V(C)$ has a perfect matching) has an odd number of edges oriented in either direction of the cycle. It is known that the number of perfect matchings of a Pfaffian graph can be computed in polynomial time. In this paper, we show that every embedding of a Pfaffian brace (i.e. 2-extendable bipartite graph)  on a surface with a positive genus has face-width at most 3.  Further, we study Pfaffian cubic braces and obtain a characterization of Pfaffian polyhex graphs: a polyhex graph is Pfaffian if and only if it is either non-bipartite or isomorphic to the cube, or the Heawood graph, or the Cartesian product $C_k\times K_2$ for even integers $k\ge 6$.


2012 ◽  
Vol 7 (1) ◽  
pp. 174-197 ◽  
Author(s):  
Heather Small ◽  
Kristine Kasianovitz ◽  
Ronald Blanford ◽  
Ina Celaya

Social networking sites and other social media have enabled new forms of collaborative communication and participation for users, and created additional value as rich data sets for research. Research based on accessing, mining, and analyzing social media data has risen steadily over the last several years and is increasingly multidisciplinary; researchers from the social sciences, humanities, computer science and other domains have used social media data as the basis of their studies. The broad use of this form of data has implications for how curators address preservation, access and reuse for an audience with divergent disciplinary norms related to privacy, ownership, authenticity and reliability.In this paper, we explore how the characteristics of the Twitter platform, coupled with an ambiguous and evolving understanding of privacy in networked communication, and divergent disciplinary understandings of the resulting data, combine to create complex issues for curators trying to ensure broad-based and ethical reuse of Twitter data. We provide a case study of a specific data set to illustrate how data curators can engage with the topics and questions raised in the paper. While some initial suggestions are offered to librarians and other information professionals who are beginning to receive social media data from researchers, our larger goal is to stimulate discussion and prompt additional research on the curation and preservation of social media data.


2016 ◽  
Vol 69 (5) ◽  
pp. 1143-1153 ◽  
Author(s):  
Marta Wlodarczyk–Sielicka ◽  
Andrzej Stateczny

An electronic navigational chart is a major source of information for the navigator. The component that contributes most significantly to the safety of navigation on water is the information on the depth of an area. For the purposes of this article, the authors use data obtained by the interferometric sonar GeoSwath Plus. The data were collected in the area of the Port of Szczecin. The samples constitute large sets of data. Data reduction is a procedure to reduce the size of a data set to make it easier and more effective to analyse. The main objective of the authors is the compilation of a new reduction algorithm for bathymetric data. The clustering of data is the first part of the search algorithm. The next step consists of generalisation of bathymetric data. This article presents a comparison and analysis of results of clustering bathymetric data using the following selected methods:K-means clustering algorithm, traditional hierarchical clustering algorithms and self-organising map (using artificial neural networks).


2020 ◽  
Vol 33 (8) ◽  
pp. 1815-1834
Author(s):  
Natalie Elms ◽  
Gavin Nicholson

PurposeThe purpose of this paper is to explore why different directors feel different levels of accountability toward board tasks.Design/methodology/approachThe paper employs a reflexive three wave data and analysis process culminating in a rich data set of 49 interviews with Australian directors and 15 h of boardroom observations.FindingsDifferences in role identification lead directors to perceive their accountability differently resulting in wide variation in levels of firm specific knowledge, eventually affecting their breadth of contribution to board tasks.Research limitations/implicationsResearchers should question the application of traditional governance theory (such as agency theory) if it fails to account for individual differences in intrinsic self-interest.Practical implicationsSelecting board members for their functional knowledge alone may not always produce optimal outcomes for the board and firm. Board induction processes and ongoing director training are important tools to inform and remind directors of their role and accountabilities on a board.Originality/valueThis paper establishes that the strength of directors' identification with either the director role or expert role affects what they feel accountable for, the development of firm specific knowledge and long-term efficacy as a director.


2018 ◽  
Vol 6 (1) ◽  
pp. 343-356
Author(s):  
K. Arathi Bhat ◽  
G. Sudhakara

Abstract In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GPk , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GPk ) is realizable as a graph if and only if P satis_es perfect matching property. For A(G)A(GPk ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GPk and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GPk is a graph of rank r and A(G)A(GPk ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.


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