---
_id: '177'
abstract:
- lang: eng
text: 'Efficiently parallelizable parameterized problems have been classified as
being either in the class FPP (fixed-parameter parallelizable) or the class PNC
(parameterized analog of NC), which contains FPP as a subclass. In this paper,
we propose a more restrictive class of parallelizable parameterized problems called
fixed-parameter parallel-tractable (FPPT). For a problem to be in FPPT, it should
possess an efficient parallel algorithm not only from a theoretical standpoint
but in practice as well. The primary distinction between FPPT and FPP is the parallel
processor utilization, which is bounded by a polynomial function in the case of
FPPT. We initiate the study of FPPT with the well-known k-vertex cover problem.
In particular, we present a parallel algorithm that outperforms the best known
parallel algorithm for this problem: using O(m) instead of O(n2) parallel processors,
the running time improves from 4logn+O(kk) to O(k⋅log3n), where m is the number
of edges, n is the number of vertices of the input graph, and k is an upper bound
of the size of the sought vertex cover. We also note that a few P-complete problems
fall into FPPT including the monotone circuit value problem (MCV) when the underlying
graphs are bounded by a constant Euler genus.'
author:
- first_name: Faisal N.
full_name: Abu-Khzam, Faisal N.
last_name: Abu-Khzam
- first_name: Shouwei
full_name: Li, Shouwei
last_name: Li
- first_name: Christine
full_name: Markarian, Christine
id: '37612'
last_name: Markarian
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Pavel
full_name: Podlipyan, Pavel
last_name: Podlipyan
citation:
ama: 'Abu-Khzam FN, Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. On the
Parameterized Parallel Complexity and the Vertex Cover Problem. In: *Proceedings
of the 10th International Conference on Combinatorial Optimization and Applications
(COCOA)*. LNCS. ; 2016:477-488. doi:10.1007/978-3-319-48749-6_35'
apa: Abu-Khzam, F. N., Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan,
P. (2016). On the Parameterized Parallel Complexity and the Vertex Cover Problem.
In *Proceedings of the 10th International Conference on Combinatorial Optimization
and Applications (COCOA)* (pp. 477–488). https://doi.org/10.1007/978-3-319-48749-6_35
bibtex: '@inproceedings{Abu-Khzam_Li_Markarian_Meyer auf der Heide_Podlipyan_2016,
series={LNCS}, title={On the Parameterized Parallel Complexity and the Vertex
Cover Problem}, DOI={10.1007/978-3-319-48749-6_35},
booktitle={Proceedings of the 10th International Conference on Combinatorial Optimization
and Applications (COCOA)}, author={Abu-Khzam, Faisal N. and Li, Shouwei and Markarian,
Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2016},
pages={477–488}, collection={LNCS} }'
chicago: Abu-Khzam, Faisal N., Shouwei Li, Christine Markarian, Friedhelm Meyer
auf der Heide, and Pavel Podlipyan. “On the Parameterized Parallel Complexity
and the Vertex Cover Problem.” In *Proceedings of the 10th International Conference
on Combinatorial Optimization and Applications (COCOA)*, 477–88. LNCS, 2016.
https://doi.org/10.1007/978-3-319-48749-6_35.
ieee: F. N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan,
“On the Parameterized Parallel Complexity and the Vertex Cover Problem,” in *Proceedings
of the 10th International Conference on Combinatorial Optimization and Applications
(COCOA)*, 2016, pp. 477–488.
mla: Abu-Khzam, Faisal N., et al. “On the Parameterized Parallel Complexity and
the Vertex Cover Problem.” *Proceedings of the 10th International Conference
on Combinatorial Optimization and Applications (COCOA)*, 2016, pp. 477–88,
doi:10.1007/978-3-319-48749-6_35.
short: 'F.N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan,
in: Proceedings of the 10th International Conference on Combinatorial Optimization
and Applications (COCOA), 2016, pp. 477–488.'
date_created: 2017-10-17T12:41:26Z
date_updated: 2022-01-06T06:53:17Z
ddc:
- '000'
department:
- _id: '63'
doi: 10.1007/978-3-319-48749-6_35
file:
- access_level: closed
content_type: application/pdf
creator: ups
date_created: 2018-11-02T14:15:18Z
date_updated: 2018-11-02T14:15:18Z
file_id: '5266'
file_name: OnTheParameterizedParallelComp.pdf
file_size: 293345
relation: main_file
success: 1
file_date_updated: 2018-11-02T14:15:18Z
has_accepted_license: '1'
language:
- iso: eng
page: 477-488
project:
- _id: '1'
name: SFB 901
- _id: '5'
name: SFB 901 - Subprojekt A1
- _id: '2'
name: SFB 901 - Project Area A
publication: Proceedings of the 10th International Conference on Combinatorial Optimization
and Applications (COCOA)
series_title: LNCS
status: public
title: On the Parameterized Parallel Complexity and the Vertex Cover Problem
type: conference
user_id: '477'
year: '2016'
...