scholarly journals Recognizing Hole-Free 4-Map Graphs in Cubic Time

Algorithmica ◽  
2006 ◽  
Vol 45 (2) ◽  
pp. 227-262 ◽  
Author(s):  
Zhi-Zhong Chen ◽  
Michelangelo Grigni ◽  
Christos H. Papadimitriou
Keyword(s):  
Map Graphs

scholarly journals Twin-width I: Tractable FO Model Checking

2022 ◽  
Vol 69 (1) ◽  
pp. 1-46
Author(s):  
Édouard Bonnet ◽  
Eun Jung Kim ◽  
Stéphan Thomassé ◽  
Rémi Watrigant
Keyword(s):  
Model Checking ◽  
Elementary Function ◽  
First Order ◽  
Fpt Algorithm ◽  
Fixed Parameter ◽  
Dimension 2 ◽  
Bounded Size ◽  
Map Graphs ◽  
Dimensional Ball ◽  
Bounded Width

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of d -contractions , witness that the twin-width is at most d . We show that FO model checking, that is deciding if a given first-order formula ϕ evaluates to true for a given binary structure G on a domain D , is FPT in |ϕ| on classes of bounded twin-width, provided the witness is given. More precisely, being given a d -contraction sequence for G , our algorithm runs in time f ( d ,|ϕ |) · |D| where f is a computable but non-elementary function. We also prove that bounded twin-width is preserved under FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS’15].

scholarly journals Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs

2003 ◽  
pp. 829-844 ◽  
Author(s):  
Erik D. Demaine ◽  
Fedor V. Fomin ◽  
Mohammad Taghi Hajiaghayi ◽  
Dimitrios M. Thilikos
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Map Graphs

Characterizing and Recognizing 4-Map Graphs

Algorithmica ◽  
2018 ◽  
Vol 81 (5) ◽  
pp. 1818-1843 ◽  
Author(s):  
Franz J. Brandenburg
Keyword(s):  
Map Graphs

scholarly journals Linear Operators That Preserve the Genus of a Graph

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 312 ◽  
Author(s):  
LeRoy Beasley ◽  
Jeong Kim ◽  
Seok-Zun Song
Keyword(s):  
Linear Operator ◽  
Orientable Surface ◽  
Linear Operators ◽  
Map Graphs ◽  
Edge Crossings

A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k − 1 . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 . We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion.

scholarly journals Fixed-parameter algorithms for ( k , r )-center in planar graphs and map graphs

2005 ◽  
Vol 1 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Erik D. Demaine ◽  
Fedor V. Fomin ◽  
Mohammadtaghi Hajiaghayi ◽  
Dimitrios M. Thilikos
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Map Graphs

scholarly journals 3 Barrier free visibility for staff in ICU Focused on space syntax for circulation in Asian ICU

2014 ◽  
Vol 1 (1) ◽  
pp. 9
Author(s):  
Javaria Manzoor Shaikh
Keyword(s):  
Intensive Care Unit ◽  
Intensive Care ◽  
Medical Intensive Care Unit ◽  
Space Syntax ◽  
Depth Map ◽  
Space Distribution ◽  
Optimal Conditions ◽  
Panoramic View ◽  
Medical Intensive Care ◽  
Map Graphs

The main contribution of paper is for designersthrough identification of appropriate shape geometry required forcare givers in a hospital by using space syntax technique.Healthcare management field is at a boom now a days, andfacilitating nurse is one of the important aspect coming up infuture, thus a lot of new courses in this field are also beenintroduced and management is in demand. Focus is on creatingthe optimal conditions for innovation in healthcare, which hasmore to do with team dynamics and mindset than standardprocesses and tools. Researchers are rigorously working toimprove patient safety by increasing and improving interface withnurse. This study systematically analyses the Nurse Stationtypo-morphology, and simulates nurse vision. The visualconnectivity is measured on depth map graphs. Hence the aim isto reduce staff stress and fatigue by support space distribution byincreasing effectiveness in delivering care. A depth mapcomparative analysis of three types of the Surgical Intensive CareUnit (SICU), Medical Intensive Care Unit MICU and CriticalCare Unit CCU found at hospitals Hallym University MedicalCenter, South Korea (HUMC), is analyzed here. Concussively, itwas proved that L-Shape provides maximum visibility, where as Ishape provides vast vista of a panoramic view from the NurseStation.

scholarly journals Linear Operators That Preserve Two Genera of a Graph

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 676
Author(s):  
LeRoy B. Beasley ◽  
Kyung-Tae Kang ◽  
Seok-Zun Song
Keyword(s):  
Linear Operator ◽  
Orientable Surface ◽  
Linear Operators ◽  
Empty Graph ◽  
Map Graphs ◽  
Edge Crossings

If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus g − 1 without edge crossings, then we say that the graph has genus g. We consider a mapping on the set of graphs with m vertices into itself. The mapping is called a linear operator if it preserves a union of graphs and it also preserves the empty graph. On the set of graphs with m vertices, we consider and investigate those linear operators which map graphs of genus g to graphs of genus g and graphs of genus g + j to graphs of genus g + j for j ≤ g and m sufficiently large. We show that such linear operators are necessarily vertex permutations.

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