Improved approaches to the exact solution of the machine covering problem

2016 ◽  
Vol 20 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Rico Walter ◽  
Martin Wirth ◽  
Alexander Lawrinenko
Keyword(s):  
Exact Solution ◽  
Covering Problem ◽  
Machine Covering

MapReduce machine covering problem on a small number of machines

2019 ◽  
Vol 38 (4) ◽  
pp. 1066-1076
Author(s):  
Yiwei Jiang ◽  
Ping Zhou ◽  
Wei Zhou
Keyword(s):  
Covering Problem ◽  
Machine Covering

GRAPH ORIENTATION TO MAXIMIZE THE MINIMUM WEIGHTED OUTDEGREE

2011 ◽  
Vol 22 (03) ◽  
pp. 583-601 ◽  
Author(s):  
YUICHI ASAHIRO ◽  
JESPER JANSSON ◽  
EIJI MIYANO ◽  
HIROTAKA ONO
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Job Scheduling ◽  
Weighted Graph ◽  
Exact Algorithm ◽  
Covering Problem ◽  
Graph Orientation ◽  
Cactus Graph ◽  
New Variant ◽  
Machine Covering

We study a new 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 – ε for any constant ε > 0 in polynomial time unless P = NP , even if all edge weights belong to {1, 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 [Formula: see text]-approximation algorithm for MAXMINO where wmax and wmin 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 wmin 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.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model

Unsteady Exact Solution for Flows of Fluids with Pressure-Dependent Viscosities

2006 ◽  
Vol 106 (2) ◽  
pp. 115-130 ◽  
Author(s):  
K. R. Rajagopal ◽  
G. Saccomandi
Keyword(s):  
Exact Solution
Sign in / Sign up

Export Citation Format

Share Document