Complexity analysis and algorithms for the Program Download Problem
In this paper, we consider the Program Download Problem (PDP) which is to download a set of desired programs from multiple channels. When the problem is to decide whether the download can be done by a given deadline d and each program appears in each of the n channels at most once, denoted as PDP (...
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| Vydáno v: | Journal of combinatorial optimization Ročník 29; číslo 1; s. 216 - 227 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.01.2015
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| ISSN: | 1382-6905, 1573-2886 |
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| Abstract | In this paper, we consider the Program Download Problem (PDP) which is to download a set of desired programs from multiple channels. When the problem is to decide whether the download can be done by a given deadline
d
and each program appears in each of the
n
channels at most once, denoted as
PDP
(
n
,
1
,
d
)
, we prove that
PDP
(
n
,
1
,
d
)
is NP-complete by a reduction from 3-SAT(3). We can extend the NP-hardness proof to
PDP
(
2
,
3
,
d
)
where there are only two channels but each program could appear in each channel at most 3 times, although
PDP
(
2
,
1
,
d
)
and
PDP
(
2
,
2
,
d
)
are both in
P
. We show that the aligned version of the problem (APDP) is polynomially solvable by reducing it to a maximum flow problem. For a different version of the problem, MPDP, where the objective is to maximize the number of program downloaded before a given deadline
d
, we prove that it is fixed-parameter tractable. Finally, we devise an approximation algorithm for
MPDP
(
2
,
p
,
d
)
,
p
≥
3
, which aims to maximize the number of desired programs downloaded in two channels. |
|---|---|
| AbstractList | In this paper, we consider the Program Download Problem (PDP) which is to download a set of desired programs from multiple channels. When the problem is to decide whether the download can be done by a given deadline
d
and each program appears in each of the
n
channels at most once, denoted as
PDP
(
n
,
1
,
d
)
, we prove that
PDP
(
n
,
1
,
d
)
is NP-complete by a reduction from 3-SAT(3). We can extend the NP-hardness proof to
PDP
(
2
,
3
,
d
)
where there are only two channels but each program could appear in each channel at most 3 times, although
PDP
(
2
,
1
,
d
)
and
PDP
(
2
,
2
,
d
)
are both in
P
. We show that the aligned version of the problem (APDP) is polynomially solvable by reducing it to a maximum flow problem. For a different version of the problem, MPDP, where the objective is to maximize the number of program downloaded before a given deadline
d
, we prove that it is fixed-parameter tractable. Finally, we devise an approximation algorithm for
MPDP
(
2
,
p
,
d
)
,
p
≥
3
, which aims to maximize the number of desired programs downloaded in two channels. |
| Author | Zhou, Jie Peng, Chao Zhu, Binhai Zhu, Hong |
| Author_xml | – sequence: 1 givenname: Chao surname: Peng fullname: Peng, Chao organization: Software Engineering Institute, East China Normal University – sequence: 2 givenname: Jie surname: Zhou fullname: Zhou, Jie email: jiezhou@shnu.edu.cn organization: Mathematics and Science College, Shanghai Normal University – sequence: 3 givenname: Binhai surname: Zhu fullname: Zhu, Binhai organization: Department of Computer Science, Montana State University – sequence: 4 givenname: Hong surname: Zhu fullname: Zhu, Hong organization: Software Engineering Institute, East China Normal University |
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| Keywords | FPT algorithm NP-complete Program Download Problem Approximation algorithm |
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| References | GareyMRJohnsonDSComputers and intractability: a guide to the theory of NP-completeness1979New YorkW. H. Freeman and Company0411.68039 PengCShenHA new approximation algorithm for computing 2-restricted disjoint pathsIEICE Trans Inf Syst2007E90–D246547210.1093/ietisy/e90-d.2.465 Lu ZX, Shi Y, Wu WL, Fu B (2012) Efficient data retrieval scheduling for multi-channel wireless data broadcast. In: Proceedings of the 31st IEEE international conference on computer communications (INFOCOM), pp 891–899 PapadimitriouCHComputational complexity1994New YorkAddison-Wesley0833.68049 ViswanathanSImielinskiTMetropolitan area video-on-demand service using pyramid broadcastingMultimed Syst19964419720810.1007/s005300050023 Aggarwal CC, Wolf JL, Yu PS (1996) A permutation-based pyramid broadcasting scheme for video-on-demand systems. In: Proceedings of the international conference on multimedia computing and systems, pp 118–26 JuhnLTsengLHarmonic broadcasting for video-on-demand serviceIEEE Trans Broadcast199743326827110.1109/11.632927 AlmerothKCAmmarMHThe use of multicast delivery to provide a scalable and interactive video-on-demand serviceIEEE J Sel Areas Commun19961451110112210.1109/49.508282 KaragiannisGAltintasOEkiciEHeijenkGJarupanBLinKWeilTVehicular networking: a survey and tutorial on requirements, architectures, challenges, standards and solutionsIEEE Commun Surv Tutor201113458461610.1109/SURV.2011.061411.00019 Hua KA, Sheu S (1997) Skyscraper broadcasting: a new broadcasting scheme for metropolitan video-on-demand systems. In: Proceedings of the ACM SIGCOMM ’97 conference, Cannes, pp 89–100 InoueMOhnishiMPengCLiRMorinoHNerveNet: a future regional platform network for various context-aware services with sensors and actuatorsIEICE Trans Commun2011E94–B361862910.1587/transcom.E94.B.618 DowneyRGFellowsMRParameterized complexity1999New YorkSpringer10.1007/978-1-4612-0515-9 LuZXWuWLFuBOptimal data retrieval scheduling in the multi-channel data broadcast environmentsIEEE Trans Comput2013621224272439 PengCTanYXiongNXYangLTParkJHKimSSAdaptive video-on-demand broadcasting in ubiquitous computing environmentJ Pers Ubiq Comput200913747948810.1007/s00779-009-0227-6 AhujaRKMagnantiTLOrlinJBNetworks flows1993Englewood CliffsPrentice-Hall ToveyCAA simplified NP-complete satisfiability problemDiscret Appl Math198481858910.1016/0166-218X(84)90081-70534.68028739601 CH Papadimitriou (9702_CR12) 1994 C Peng (9702_CR13) 2007; E90–D L Juhn (9702_CR8) 1997; 43 KC Almeroth (9702_CR3) 1996; 14 9702_CR6 G Karagiannis (9702_CR9) 2011; 13 9702_CR1 RG Downey (9702_CR4) 1999 M Inoue (9702_CR7) 2011; E94–B RK Ahuja (9702_CR2) 1993 S Viswanathan (9702_CR16) 1996; 4 MR Garey (9702_CR5) 1979 9702_CR10 9702_CR11 CA Tovey (9702_CR15) 1984; 8 C Peng (9702_CR14) 2009; 13 |
| References_xml | – reference: Lu ZX, Shi Y, Wu WL, Fu B (2012) Efficient data retrieval scheduling for multi-channel wireless data broadcast. In: Proceedings of the 31st IEEE international conference on computer communications (INFOCOM), pp 891–899 – reference: JuhnLTsengLHarmonic broadcasting for video-on-demand serviceIEEE Trans Broadcast199743326827110.1109/11.632927 – reference: PengCTanYXiongNXYangLTParkJHKimSSAdaptive video-on-demand broadcasting in ubiquitous computing environmentJ Pers Ubiq Comput200913747948810.1007/s00779-009-0227-6 – reference: ViswanathanSImielinskiTMetropolitan area video-on-demand service using pyramid broadcastingMultimed Syst19964419720810.1007/s005300050023 – reference: LuZXWuWLFuBOptimal data retrieval scheduling in the multi-channel data broadcast environmentsIEEE Trans Comput2013621224272439 – reference: KaragiannisGAltintasOEkiciEHeijenkGJarupanBLinKWeilTVehicular networking: a survey and tutorial on requirements, architectures, challenges, standards and solutionsIEEE Commun Surv Tutor201113458461610.1109/SURV.2011.061411.00019 – reference: AlmerothKCAmmarMHThe use of multicast delivery to provide a scalable and interactive video-on-demand serviceIEEE J Sel Areas Commun19961451110112210.1109/49.508282 – reference: InoueMOhnishiMPengCLiRMorinoHNerveNet: a future regional platform network for various context-aware services with sensors and actuatorsIEICE Trans Commun2011E94–B361862910.1587/transcom.E94.B.618 – reference: PengCShenHA new approximation algorithm for computing 2-restricted disjoint pathsIEICE Trans Inf Syst2007E90–D246547210.1093/ietisy/e90-d.2.465 – reference: AhujaRKMagnantiTLOrlinJBNetworks flows1993Englewood CliffsPrentice-Hall – reference: GareyMRJohnsonDSComputers and intractability: a guide to the theory of NP-completeness1979New YorkW. H. Freeman and Company0411.68039 – reference: DowneyRGFellowsMRParameterized complexity1999New YorkSpringer10.1007/978-1-4612-0515-9 – reference: PapadimitriouCHComputational complexity1994New YorkAddison-Wesley0833.68049 – reference: Hua KA, Sheu S (1997) Skyscraper broadcasting: a new broadcasting scheme for metropolitan video-on-demand systems. In: Proceedings of the ACM SIGCOMM ’97 conference, Cannes, pp 89–100 – reference: Aggarwal CC, Wolf JL, Yu PS (1996) A permutation-based pyramid broadcasting scheme for video-on-demand systems. In: Proceedings of the international conference on multimedia computing and systems, pp 118–26 – reference: ToveyCAA simplified NP-complete satisfiability problemDiscret Appl Math198481858910.1016/0166-218X(84)90081-70534.68028739601 – ident: 9702_CR1 doi: 10.1109/MMCS.1996.534963 – volume: 8 start-page: 85 issue: 1 year: 1984 ident: 9702_CR15 publication-title: Discret Appl Math doi: 10.1016/0166-218X(84)90081-7 – volume: 13 start-page: 479 issue: 7 year: 2009 ident: 9702_CR14 publication-title: J Pers Ubiq Comput doi: 10.1007/s00779-009-0227-6 – volume-title: Networks flows year: 1993 ident: 9702_CR2 – ident: 9702_CR6 – volume: E94–B start-page: 618 issue: 3 year: 2011 ident: 9702_CR7 publication-title: IEICE Trans Commun doi: 10.1587/transcom.E94.B.618 – volume: 43 start-page: 268 issue: 3 year: 1997 ident: 9702_CR8 publication-title: IEEE Trans Broadcast doi: 10.1109/11.632927 – volume: 13 start-page: 584 issue: 4 year: 2011 ident: 9702_CR9 publication-title: IEEE Commun Surv Tutor doi: 10.1109/SURV.2011.061411.00019 – volume-title: Computational complexity year: 1994 ident: 9702_CR12 – volume-title: Parameterized complexity year: 1999 ident: 9702_CR4 doi: 10.1007/978-1-4612-0515-9 – ident: 9702_CR11 doi: 10.1109/TC.2012.139 – ident: 9702_CR10 – volume: 14 start-page: 1110 issue: 5 year: 1996 ident: 9702_CR3 publication-title: IEEE J Sel Areas Commun doi: 10.1109/49.508282 – volume: 4 start-page: 197 issue: 4 year: 1996 ident: 9702_CR16 publication-title: Multimed Syst doi: 10.1007/s005300050023 – volume: E90–D start-page: 465 issue: 2 year: 2007 ident: 9702_CR13 publication-title: IEICE Trans Inf Syst doi: 10.1093/ietisy/e90-d.2.465 – volume-title: Computers and intractability: a guide to the theory of NP-completeness year: 1979 ident: 9702_CR5 |
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| SubjectTerms | Combinatorics Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation |
| Title | Complexity analysis and algorithms for the Program Download Problem |
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