Degree-constrained spanners for multidimensional grids

AbstractA spanning subgraph S = (V, E′) of a connected simple graph G = (V, E) is a f (x) -spanner if for any pair of nodes u and v, ds(u, v) ⩽ f (dG(u, v)) where dG and ds are the usual distance functions in graphs G and S, respectively. The delay of the f (x) -spanner is f(x) − x. We construct four spanners with maximum degree 4 for infinite d-dimensional grids with delays 2d − 4, 2⌈d2⌉ + 2[(d − 2)/4] + 2, 2⌈(d − 6)/8⌉ + 4⌈d + 1)/4⌉+ 6, and ⌈(⌈d/2⌉ + 1)/ (1 + 1)rl + 2⌈ d2⌉ + 21 + 2. All of these constructions can be modified to produce spanners of finite (d-dimensional grids with essentially the same delay. We also construct a (5d + 4 + x) -spanner with maximum degree 3 for infinite d-dimensional grids. This construction can be used to produce spanners of finite d-dimensional grids where all dimensions are even with the same delay. We prove an Ω(d) lower bound for the delay of maximum degree 3 or 4 spanners of finite or infinite d-dimensional grids. For the particular cases of infinite 3- and 4-dimensional grids, we construct (6 + x) -spanners and (14 + x) -spanners, respectively. The former can be modified to construct a (6 + x) -spanner of a finite 3-dimensional grid where all dimensions are even or where all dimensions are odd and a (8 + x) -spanner of a finite 3-dimensional grid otherwise. The latter yields (14 + x) -spanners of finite 4-dimensional grids where all dimensions are even

Edge-disjoint spanners in Cartesian products of graphs

AbstractA spanning subgraph S=(V,E′) of a connected graph G=(V,E) is an (x+c)-spanner if for any pair of vertices u and v, dS(u,v)⩽dG(u,v)+c where dG and dS are the usual distance functions in G and S, respectively. The parameter c is called the delay of the spanner. We study edge-disjoint spanners in graphs, focusing on graphs formed as Cartesian products. Our approach is to construct sets of edge-disjoint spanners in a product based on sets of edge-disjoint spanners and colorings of the component graphs. We present several results on general products and then narrow our focus to hypercubes

The Symbiotic Existence of Interorganizational and Interpersonal Networks in Collaboration

Most traditional theories adopted to explain collaboration in interorganizational relationships (IOR) have failed to adequately address the micro and macro dynamics of the phenomenon. Collaboration theory developed within the mainstream of public administration research views leveraging structure, processes, and people as the key to successful collaboration. Yet, the applicability of the theory’s principles and abstractions in the private sector remains unexplored. Social network theory also presumes that IOR arise out of ongoing interaction at both micro and macro levels. However, the field is fragmented, with the interpersonal and interorganizational networks being studied separately. Thus, an opportunity exists to combine collaboration theory with social network perspective and to view interorganizational collaboration from a multilevel lens. An exploratory case study methodology informed by an interpretivist epistemological stance was used to address this gap. An egocentric network of a third party logistics company that covers six relationships provided a rich context for the study. The study finding expands our understanding of the distinction between the two types of networks: the interorganizational and the interpersonal and their corresponding elements - which are the structural and processual ties and the workflow and commercial friendship ties rspectively. By proposing a new conceptualization ─ ‘a symbiotic existence’ to explain the interdependent nature of these four elements, the study goes beyond the traditional micro and macro divide to consider the multiplexity of networks in IOR.The major practical implication of this study is that the decision makers should pay attention to the changes in both micro and macro elements and their knock-on effects to ensure a symbiosis of the four elements for collaborative synergies. Practitioners’ attention should also centre significantly on the effects of interpersonal networks on collaboration and how mechanisms at macro level could be set effectively to benefit from the emerging community of practices within the collaboration

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Frugal innovation for healthcare: strategies and tools for the identification and evaluation of frugal and reverse innovations in healthcare

Global healthcare systems are united by their desire to widen patient access to safe and effective clinical services in the face of increasing demand and financial constraints. In low- and middle-income countries (LMICs), a variety of ingenious product and process solutions, termed frugal innovations, have been able to deliver services at a fraction of the cost. It is the broad proposition of this work that such ideas could be applicable to high-income countries (HICs), a concept labeled reverse innovation. Using a conceptual model of innovation scouting derived from the causal mechanism of critical realism, this work examined the development and testing of a tool to deductively identify frugal innovations in healthcare (FIH-ID tool) and then evaluated methodology to assess the reversibility of potential of frugal innovations. The FIH-ID tool demonstrated consistently acceptable inter-rater reliability scores using different methods of application and different raters, moreover, construct validity was shown by its ability to identify well-known frugal innovations. With respect to the assessment of the reversibility potential, the results of the present study highlighted the challenges of undertaking such a complex evaluation process using a simple scoring system. Raters achieved poor levels of inter-rater reliability and only 2 innovations were thought likely to reverse to a HIC. This study presents the first application of a critical realist approach to innovation scouting. It has identified a cohort of 76 potential frugal innovations in healthcare suggesting that the FIH-ID tool is likely to be a valuable asset for similar studies in the future. It has highlighted the challenges of assessing the reversibility potential of innovations from LMICs. It has documented the emergence of the global innovation curator, entities that seek to identify, curate and promote innovations from LMICs, and it proposes a conceptual model for the role of global innovation curators in the diffusion of innovation.Open Acces

The Historical Development Of Strategic Planning Theories

This paper discusses both broad historical and philosophical theories of strategic management, as well as specific communication and human resource management theories and practices. It concludes with an application chapter emphasizing how the Roman Catholic Church needs to develop a strategy to integrate learning and innovation in order to reconcile and communicate its central message locally. Although built upon a hierarchical and organizational culture, where strict obedience to institutional directives dominates the communities it serves, the diversity within the Church is forcing the Vatican to ensure specialized sub-cultures are not polarized

The social reality of initiatives which pursue insight from data

While (big) data promises immense opportunity, initiatives focused on using data to pursue insight have mixed outcomes. The Management Support Systems (MSS) model summarises what we currently understand within Information Systems (IS) about the implementation and use of systems to improve organisations’ use of data. Adopting an ethnographic approach to observe how practitioners in two contrasting organisations actually generate insight from data, this research challenges the implicit information processing and implementation logics of the MMS model. The pragmatic messiness of pursuing insight is described in two monographs, which reveal the socially constructed nature of data in relation to phenomena, and the importance of data engagement to produce insight. Given that this PhD study also seeks to generate insight from data, it is compared and contrasted reflexively to the two cases observed. While the inquiry logic pursued in this study was made explicit, and was regularly reviewed and challenged, the two cases left this largely implicit. The use of tools is shown to facilitate and constrain inquiry, with related data acting as boundary objects between the different practitioner groups involved. An explanatory framework is presented and used to suggest various enhancements to the MSS model. First, the Problem Space is reframed to reflect the distinct, though interdependent logics involved in inquiry versus realising envisaged benefits from insights. Second, the MSS artefact itself is contextualised and Data Engagement rather than MSS or Tool Use is positioned as central. Third, Data are disentangled from the wider MSS artefact, as a critical, distinct construct. Fourth, an Alignment construct is introduced to address the boundary spanning nature of data initiatives. The thesis also highlights the value of using Wenger’s (1998) Communities of Practice (CoP) situated learning framework to study data initiatives, and the related value of mapping groups as a technique for further development. Some questions are provided for practitioners to gain a better understanding of data initiatives. Wider implications are also noted for the socio-material theorising of Data, and distinguishing between Data, Information and Knowledge concepts within the IS discipline