NDLI: Graph orientation to maximize the minimum weighted outdegree

Content Provider	IEEE Xplore Digital Library
Author	Asahiro, Y. Jansson, J. Miyano, E. Ono, H.
Copyright Year	2009
Description	Author affiliation: Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan (Jansson, J.) \|\| Department of System Design and Informatics, Kyushu Institute of Technology, Iizuka, Fukuoka 820-8502, Japan (Miyano, E.) \|\| Department of Computer Science and Communication Engineering, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan (Ono, H.) \|\| Department of Social Information Systems, Kyushu Sangyo University, Higashi-ku, Fukuoka 813-8503, Japan (Asahiro, Y.)
Abstract	We study a new a variant of the graph orientation problem called MAXMINO where the input is an undirected, edge-weighted graph and the objective is to assign a direction to each edge so that the minimum weighted outdegree (taken over all vertices in the resulting directed graph) is maximized. All edge weights are assumed to be positive integers. This problem is closely related to the job scheduling on parallel machines, called the machine covering problem, where its goal is to assign jobs to parallel machines such that each machine is covered as much as possible. First, we prove that MAXMINO is strongly NP-hard and cannot be approximated within a ratio of 2 = ∈ for constant ∈ ≫ 0 in polynomial time unless P=NP, even if all edge weights belong to {2}, every vertex has degree at most three, and the input graph is bipartite or planar. Next, we show how to solve MAXMINO exactly in polynomial time for the special case in which all edge weights are equal to 1. This technique gives us a simple polynomial-time w-approximation algorithm for MAXMINO where w and w denote the maximum and minimum weights among all the input edges. Furthermore. we also observe that this approach yields an exact algorithm for the general case of MAXMINO whose running time is polynomial whenever the number of edges having weight larger than w is at most logarithmic in the number of vertices. Finally, we, show that MAXMINO is solvable in polynomial time if the input is a cactus graph.
Starting Page	1
Ending Page	8
File Size	278931
Page Count	8
File Format	PDF
ISBN	9781424437511
ISSN	15302075
DOI	10.1109/IPDPS.2009.5160872
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-05-23
Publisher Place	Italy
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Parallel machines Approximation algorithms
Content Type	Text
Resource Type	Article

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