Please wait, while we are loading the content...
Please wait, while we are loading the content...
Content Provider | ACM Digital Library |
---|---|
Author | Aichholzer, Oswin Krasser, Hannes |
Abstract | We extend the order type data base of all realizable order types in the plane to point sets of cardinality 11. More precisely, we provide a complete data base of all combinatorial different sets of up to 11 points in general position in the plane. In addition, we develop a novel and efficient method for a complete extension to order types of size 12 and more in an abstract sense, that is, without the need to store or realize the sets. The presented method is well suited for independent computations. Thus, time intensive investigations benefit from the possibility of distributed computing.Our approach has various applications to combinatorial problems which are based on sets of points in the plane. This includes classic problems like searching for (empty) convex k-gons ('happy end problem'), decomposing sets into convex regions, counting structures like triangulations or pseudo-triangulations, minimal crossing numbers, and more. We present some improved results to all these problems. As an outstanding result we have been able to determine the exact rectilinear crossing number of the complete graph Kn for up to n = 17, the largest previous range being n = 12, and slightly improved the asymptotic upper bound. |
Starting Page | 91 |
Ending Page | 98 |
Page Count | 8 |
File Format | |
ISBN | 1581139918 |
DOI | 10.1145/1064092.1064108 |
Language | English |
Publisher | Association for Computing Machinery (ACM) |
Publisher Date | 2005-06-06 |
Publisher Place | New York |
Access Restriction | Subscribed |
Subject Keyword | Complete graph Rectilinear crossing number Order type Pseudoline arrangement |
Content Type | Text |
Resource Type | Article |
National Digital Library of India (NDLI) is a virtual repository of learning resources which is not just a repository with search/browse facilities but provides a host of services for the learner community. It is sponsored and mentored by Ministry of Education, Government of India, through its National Mission on Education through Information and Communication Technology (NMEICT). Filtered and federated searching is employed to facilitate focused searching so that learners can find the right resource with least effort and in minimum time. NDLI provides user group-specific services such as Examination Preparatory for School and College students and job aspirants. Services for Researchers and general learners are also provided. NDLI is designed to hold content of any language and provides interface support for 10 most widely used Indian languages. It is built to provide support for all academic levels including researchers and life-long learners, all disciplines, all popular forms of access devices and differently-abled learners. It is designed to enable people to learn and prepare from best practices from all over the world and to facilitate researchers to perform inter-linked exploration from multiple sources. It is developed, operated and maintained from Indian Institute of Technology Kharagpur.
Learn more about this project from here.
NDLI is a conglomeration of freely available or institutionally contributed or donated or publisher managed contents. Almost all these contents are hosted and accessed from respective sources. The responsibility for authenticity, relevance, completeness, accuracy, reliability and suitability of these contents rests with the respective organization and NDLI has no responsibility or liability for these. Every effort is made to keep the NDLI portal up and running smoothly unless there are some unavoidable technical issues.
Ministry of Education, through its National Mission on Education through Information and Communication Technology (NMEICT), has sponsored and funded the National Digital Library of India (NDLI) project.
Sl. | Authority | Responsibilities | Communication Details |
---|---|---|---|
1 | Ministry of Education (GoI), Department of Higher Education |
Sanctioning Authority | https://www.education.gov.in/ict-initiatives |
2 | Indian Institute of Technology Kharagpur | Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project | https://www.iitkgp.ac.in |
3 | National Digital Library of India Office, Indian Institute of Technology Kharagpur | The administrative and infrastructural headquarters of the project | Dr. B. Sutradhar bsutra@ndl.gov.in |
4 | Project PI / Joint PI | Principal Investigator and Joint Principal Investigators of the project |
Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon |
5 | Website/Portal (Helpdesk) | Queries regarding NDLI and its services | support@ndl.gov.in |
6 | Contents and Copyright Issues | Queries related to content curation and copyright issues | content@ndl.gov.in |
7 | National Digital Library of India Club (NDLI Club) | Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach | clubsupport@ndl.gov.in |
8 | Digital Preservation Centre (DPC) | Assistance with digitizing and archiving copyright-free printed books | dpc@ndl.gov.in |
9 | IDR Setup or Support | Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops | idr@ndl.gov.in |
Loading...
|