scholarly journals Polynomial Time and Parameterized Approximation Algorithms for Boxicity

2012 ◽  
pp. 135-146 ◽  
Author(s):  
Abhijin Adiga ◽  
Jasine Babu ◽  
L. Sunil Chandran
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time

An FPT Algorithm for the Correlation Clustering Problem

2011 ◽  
Vol 474-476 ◽  
pp. 924-927 ◽  
Author(s):  
Xiao Xin
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Undirected Graph ◽  
Fixed Parameter Tractable ◽  
Correlation Clustering ◽  
Time Approximation ◽  
Running Time ◽  
Clustering Problem ◽  
Fpt Algorithm ◽  
Fixed Parameter

Given an undirected graph G=(V, E) with real nonnegative weights and + or – labels on its edges, the correlation clustering problem is to partition the vertices of G into clusters to minimize the total weight of cut + edges and uncut – edges. This problem is APX-hard and has been intensively studied mainly from the viewpoint of polynomial time approximation algorithms. By way of contrast, a fixed-parameter tractable algorithm is presented that takes treewidth as the parameter, with a running time that is linear in the number of vertices of G.

APPROXIMATION ALGORITHMS FOR SCHEDULING MALLEABLE TASKS UNDER PRECEDENCE CONSTRAINTS

2002 ◽  
Vol 13 (04) ◽  
pp. 613-627 ◽  
Author(s):  
RENAUD LEPÈRE ◽  
DENIS TRYSTRAM ◽  
GERHARD J. WOEGINGER
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Precedence Constraints ◽  
Performance Guarantee ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Special Cases ◽  
Special Case ◽  
Polynomial Time Approximation

This work presents approximation algorithms for scheduling the tasks of a parallel application that are subject to precedence constraints. The considered tasks are malleable which means that they may be executed on a varying number of processors in parallel. The considered objective criterion is the makespan, i.e., the largest task completion time. We demonstrate a close relationship between this scheduling problem and one of its subproblems, the allotment problem. By exploiting this relationship, we design a polynomial time approximation algorithm with performance guarantee arbitrarily close to [Formula: see text] for the special case of series parallel precedence constraints and for the special case of precedence constraints of bounded width. These special cases cover the important situation of tree structured precedence constraints. For arbitrary precedence constraints, we give a polynomial time approximation algorithm with performance guarantee [Formula: see text].

ON TWO APPROXIMATION ALGORITHMS FOR THE CLIQUE PROBLEM

1993 ◽  
Vol 04 (02) ◽  
pp. 117-133
Author(s):  
IAIN A. STEWART
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Deterministic Algorithm ◽  
Time Approximation ◽  
Nondeterministic Algorithm ◽  
Polynomial Time Approximation ◽  
Clique Problem

We look at well-known polynomial-time approximation algorithms for the optimization problem MAX-CLIQUE (“find the size of the largest clique in a graph”) with regard to how easy it is to compute the actual cliques yielded by these approximation algorithms. We show that even for two “pretty useless” deterministic polynomial-time approximation algorithms, it is unlikely that the resulting clique can be computed efficiently in parallel. We also show that for each non-deterministic algorithm, it is unlikely that there is some deterministic polynomial-time algorithm that decides whether any given vertex appears in some clique yielded by that nondeterministic algorithm.

SHORTEST DESCENDING PATHS: TOWARDS AN EXACT ALGORITHM

2011 ◽  
Vol 21 (04) ◽  
pp. 431-466 ◽  
Author(s):  
MUSTAQ AHMED ◽  
ANNA LUBIW
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Shortest Path ◽  
Exact Algorithm ◽  
Full Characterization ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
Bend Angles ◽  
Special Classes

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. Although a shortest path on a terrain unfolds to a straight line, a shortest descending path (SDP) does not. We give a full characterization of the bend angles of an SDP, showing that they follow a generalized form of Snell's law of refraction of light. The complexity of finding SDPs is open—only approximation algorithms are known. We reduce the SDP problem to the problem of finding an SDP through a given sequence of faces. We give polynomial time algorithms for SDPs on two special classes of terrains, but argue that the general case will be difficult.

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