Speeding Up the GVW Algorithm via a Substituting Method View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02

AUTHORS

Ting Li, Yao Sun, Zhenyu Huang, Dingkang Wang, Dongdai Lin

ABSTRACT

The GVW algorithm is an efficient signature-based algorithm for computing Gröbner bases. In this paper, the authors consider the implementation of the GVW algorithm by using linear algebra, and speed up GVW via a substituting method. As it is well known that, most of the computing time of a Gröbner basis is spent on reductions of polynomials. Thus, linear algebraic techniques, such as matrix operations, have been used extensively to speed up the implementations. Particularly, one-direction (also called signature-safe) reduction is used in signature-based algorithms, because polynomials (or rows in matrices) with larger signatures can only be reduced by polynomials (rows) with smaller signatures. The authors propose a new method to construct sparser matrices for signature-based algorithms via a substituting method. Specifically, instead of only storing the original polynomials in GVW, the authors also record many equivalent but sparser polynomials at the same time. In matrix construction, denser polynomials are substituted by sparser equivalent ones. As the matrices get sparser, they can be eliminated more efficiently. Two specifical algorithms, Block-GVW and LMGVW, are presented, and their combination is the Sub-GVW algorithm. The correctness of the new proposed method is proved, and the experimental results demonstrate the efficiency of this new method. More... »

PAGES

205-233

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11424-019-8345-3

DOI

http://dx.doi.org/10.1007/s11424-019-8345-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112141823


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0802", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Computation Theory and Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Chinese Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.410726.6", 
          "name": [
            "SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China", 
            "School of Cyber Security, University of Chinese Academy of Sciences, 100190, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Li", 
        "givenName": "Ting", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Information Engineering", 
          "id": "https://www.grid.ac/institutes/grid.458480.5", 
          "name": [
            "SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sun", 
        "givenName": "Yao", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Information Engineering", 
          "id": "https://www.grid.ac/institutes/grid.458480.5", 
          "name": [
            "SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Huang", 
        "givenName": "Zhenyu", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Chinese Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.410726.6", 
          "name": [
            "KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100090, Beijing, China", 
            "School of Mathematical Sciences, University of Chinese Academy of Sciences, 100190, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wang", 
        "givenName": "Dingkang", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Information Engineering", 
          "id": "https://www.grid.ac/institutes/grid.458480.5", 
          "name": [
            "SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Lin", 
        "givenName": "Dongdai", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/3-540-45539-6_27", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000285811", 
          "https://doi.org/10.1007/3-540-45539-6_27"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2010.06.019", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001338627"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2930889.2930914", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001702028"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/1576702.1576725", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002499019"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2465506.2465522", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005299081"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/780506.780516", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007436250"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-74735-2_31", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010365111", 
          "https://doi.org/10.1007/978-3-540-74735-2_31"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-74735-2_31", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010365111", 
          "https://doi.org/10.1007/978-3-540-74735-2_31"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11424-015-4085-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010484767", 
          "https://doi.org/10.1007/s11424-015-4085-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.ffa.2016.06.002", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012244299"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2011.05.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012340184"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2011.12.025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017103940"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2442829.2442860", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017577577"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-35999-6_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021725223", 
          "https://doi.org/10.1007/978-3-642-35999-6_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2010.06.013", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026421537"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-21969-6_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028053137", 
          "https://doi.org/10.1007/978-3-642-21969-6_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-21969-6_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028053137", 
          "https://doi.org/10.1007/978-3-642-21969-6_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-09519-5_52", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028563050", 
          "https://doi.org/10.1007/3-540-09519-5_52"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10623-014-9965-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030052741", 
          "https://doi.org/10.1007/s10623-014-9965-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-12868-9_99", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030833923", 
          "https://doi.org/10.1007/3-540-12868-9_99"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/1837210.1837225", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032330834"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2013.08.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033298909"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2442829.2442879", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033894307"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/11836810_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038251529", 
          "https://doi.org/10.1007/11836810_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/11836810_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038251529", 
          "https://doi.org/10.1007/11836810_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0022-4049(99)00005-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040947089"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/1837934.1837944", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042071596"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00145-011-9111-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044237636", 
          "https://doi.org/10.1007/s00145-011-9111-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11786-009-0016-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047994766", 
          "https://doi.org/10.1007/s11786-009-0016-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/1993886.1993936", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048552226"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/mcom/2969", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059342770"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-02", 
    "datePublishedReg": "2019-02-01", 
    "description": "The GVW algorithm is an efficient signature-based algorithm for computing Gr\u00f6bner bases. In this paper, the authors consider the implementation of the GVW algorithm by using linear algebra, and speed up GVW via a substituting method. As it is well known that, most of the computing time of a Gr\u00f6bner basis is spent on reductions of polynomials. Thus, linear algebraic techniques, such as matrix operations, have been used extensively to speed up the implementations. Particularly, one-direction (also called signature-safe) reduction is used in signature-based algorithms, because polynomials (or rows in matrices) with larger signatures can only be reduced by polynomials (rows) with smaller signatures. The authors propose a new method to construct sparser matrices for signature-based algorithms via a substituting method. Specifically, instead of only storing the original polynomials in GVW, the authors also record many equivalent but sparser polynomials at the same time. In matrix construction, denser polynomials are substituted by sparser equivalent ones. As the matrices get sparser, they can be eliminated more efficiently. Two specifical algorithms, Block-GVW and LMGVW, are presented, and their combination is the Sub-GVW algorithm. The correctness of the new proposed method is proved, and the experimental results demonstrate the efficiency of this new method.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11424-019-8345-3", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1053706", 
        "issn": [
          "1009-6124", 
          "1559-7067"
        ], 
        "name": "Journal of Systems Science and Complexity", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "32"
      }
    ], 
    "name": "Speeding Up the GVW Algorithm via a Substituting Method", 
    "pagination": "205-233", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "84894b7b036fabdee3191fa892eba30edced7b4ca827ef835832fa13cb0f3972"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11424-019-8345-3"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1112141823"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11424-019-8345-3", 
      "https://app.dimensions.ai/details/publication/pub.1112141823"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T09:07", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000337_0000000337/records_37570_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs11424-019-8345-3"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11424-019-8345-3'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11424-019-8345-3'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11424-019-8345-3'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11424-019-8345-3'


 

This table displays all metadata directly associated to this object as RDF triples.

185 TRIPLES      21 PREDICATES      55 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11424-019-8345-3 schema:about anzsrc-for:08
2 anzsrc-for:0802
3 schema:author Nbcf795baf9504ddba212515b03c6c4c8
4 schema:citation sg:pub.10.1007/11836810_13
5 sg:pub.10.1007/3-540-09519-5_52
6 sg:pub.10.1007/3-540-12868-9_99
7 sg:pub.10.1007/3-540-45539-6_27
8 sg:pub.10.1007/978-3-540-74735-2_31
9 sg:pub.10.1007/978-3-642-21969-6_5
10 sg:pub.10.1007/978-3-642-35999-6_2
11 sg:pub.10.1007/s00145-011-9111-4
12 sg:pub.10.1007/s10623-014-9965-1
13 sg:pub.10.1007/s11424-015-4085-1
14 sg:pub.10.1007/s11786-009-0016-7
15 https://doi.org/10.1016/j.ffa.2016.06.002
16 https://doi.org/10.1016/j.jsc.2010.06.013
17 https://doi.org/10.1016/j.jsc.2010.06.019
18 https://doi.org/10.1016/j.jsc.2011.05.004
19 https://doi.org/10.1016/j.jsc.2011.12.025
20 https://doi.org/10.1016/j.jsc.2013.08.001
21 https://doi.org/10.1016/s0022-4049(99)00005-5
22 https://doi.org/10.1090/mcom/2969
23 https://doi.org/10.1145/1576702.1576725
24 https://doi.org/10.1145/1837210.1837225
25 https://doi.org/10.1145/1837934.1837944
26 https://doi.org/10.1145/1993886.1993936
27 https://doi.org/10.1145/2442829.2442860
28 https://doi.org/10.1145/2442829.2442879
29 https://doi.org/10.1145/2465506.2465522
30 https://doi.org/10.1145/2930889.2930914
31 https://doi.org/10.1145/780506.780516
32 schema:datePublished 2019-02
33 schema:datePublishedReg 2019-02-01
34 schema:description The GVW algorithm is an efficient signature-based algorithm for computing Gröbner bases. In this paper, the authors consider the implementation of the GVW algorithm by using linear algebra, and speed up GVW via a substituting method. As it is well known that, most of the computing time of a Gröbner basis is spent on reductions of polynomials. Thus, linear algebraic techniques, such as matrix operations, have been used extensively to speed up the implementations. Particularly, one-direction (also called signature-safe) reduction is used in signature-based algorithms, because polynomials (or rows in matrices) with larger signatures can only be reduced by polynomials (rows) with smaller signatures. The authors propose a new method to construct sparser matrices for signature-based algorithms via a substituting method. Specifically, instead of only storing the original polynomials in GVW, the authors also record many equivalent but sparser polynomials at the same time. In matrix construction, denser polynomials are substituted by sparser equivalent ones. As the matrices get sparser, they can be eliminated more efficiently. Two specifical algorithms, Block-GVW and LMGVW, are presented, and their combination is the Sub-GVW algorithm. The correctness of the new proposed method is proved, and the experimental results demonstrate the efficiency of this new method.
35 schema:genre research_article
36 schema:inLanguage en
37 schema:isAccessibleForFree false
38 schema:isPartOf N47c5c6a4df0f4b2a868c0986abdcc8dd
39 N83519b4a34f7468981f584ff0add6a67
40 sg:journal.1053706
41 schema:name Speeding Up the GVW Algorithm via a Substituting Method
42 schema:pagination 205-233
43 schema:productId N01393468deb3408e8bd74f4785ca98bc
44 N755ee2cf4241477a8de6ceebe9fee3a0
45 N931e9ae886574cefa84933e2b7d7c8f8
46 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112141823
47 https://doi.org/10.1007/s11424-019-8345-3
48 schema:sdDatePublished 2019-04-11T09:07
49 schema:sdLicense https://scigraph.springernature.com/explorer/license/
50 schema:sdPublisher N30041dfaab804e25a5d400c8b89f73f3
51 schema:url https://link.springer.com/10.1007%2Fs11424-019-8345-3
52 sgo:license sg:explorer/license/
53 sgo:sdDataset articles
54 rdf:type schema:ScholarlyArticle
55 N01393468deb3408e8bd74f4785ca98bc schema:name dimensions_id
56 schema:value pub.1112141823
57 rdf:type schema:PropertyValue
58 N1e429ea8c2264ac1b7df690d9eb1b0e4 schema:affiliation https://www.grid.ac/institutes/grid.458480.5
59 schema:familyName Lin
60 schema:givenName Dongdai
61 rdf:type schema:Person
62 N1e875ca1bda444afae9b9bfd032416b1 rdf:first N20ff2dd871f8431c86dd93c73a9026bc
63 rdf:rest Nf1795e905b824e1a98a514bea5c02cd4
64 N20ff2dd871f8431c86dd93c73a9026bc schema:affiliation https://www.grid.ac/institutes/grid.458480.5
65 schema:familyName Sun
66 schema:givenName Yao
67 rdf:type schema:Person
68 N21d5aa3638814beda1325eb1796e7da6 schema:affiliation https://www.grid.ac/institutes/grid.410726.6
69 schema:familyName Wang
70 schema:givenName Dingkang
71 rdf:type schema:Person
72 N30041dfaab804e25a5d400c8b89f73f3 schema:name Springer Nature - SN SciGraph project
73 rdf:type schema:Organization
74 N425c3327f83e4385979b22e4f4027b55 schema:affiliation https://www.grid.ac/institutes/grid.410726.6
75 schema:familyName Li
76 schema:givenName Ting
77 rdf:type schema:Person
78 N47c5c6a4df0f4b2a868c0986abdcc8dd schema:issueNumber 1
79 rdf:type schema:PublicationIssue
80 N755ee2cf4241477a8de6ceebe9fee3a0 schema:name doi
81 schema:value 10.1007/s11424-019-8345-3
82 rdf:type schema:PropertyValue
83 N83519b4a34f7468981f584ff0add6a67 schema:volumeNumber 32
84 rdf:type schema:PublicationVolume
85 N8a4248c5109648518df5577c47ce1190 schema:affiliation https://www.grid.ac/institutes/grid.458480.5
86 schema:familyName Huang
87 schema:givenName Zhenyu
88 rdf:type schema:Person
89 N931e9ae886574cefa84933e2b7d7c8f8 schema:name readcube_id
90 schema:value 84894b7b036fabdee3191fa892eba30edced7b4ca827ef835832fa13cb0f3972
91 rdf:type schema:PropertyValue
92 Nbcf795baf9504ddba212515b03c6c4c8 rdf:first N425c3327f83e4385979b22e4f4027b55
93 rdf:rest N1e875ca1bda444afae9b9bfd032416b1
94 Nc5bb20c0f57a4aa4b576389977300594 rdf:first N1e429ea8c2264ac1b7df690d9eb1b0e4
95 rdf:rest rdf:nil
96 Ne539db22f8664a2c828b71dc9afe9b59 rdf:first N21d5aa3638814beda1325eb1796e7da6
97 rdf:rest Nc5bb20c0f57a4aa4b576389977300594
98 Nf1795e905b824e1a98a514bea5c02cd4 rdf:first N8a4248c5109648518df5577c47ce1190
99 rdf:rest Ne539db22f8664a2c828b71dc9afe9b59
100 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
101 schema:name Information and Computing Sciences
102 rdf:type schema:DefinedTerm
103 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
104 schema:name Computation Theory and Mathematics
105 rdf:type schema:DefinedTerm
106 sg:journal.1053706 schema:issn 1009-6124
107 1559-7067
108 schema:name Journal of Systems Science and Complexity
109 rdf:type schema:Periodical
110 sg:pub.10.1007/11836810_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038251529
111 https://doi.org/10.1007/11836810_13
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/3-540-09519-5_52 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028563050
114 https://doi.org/10.1007/3-540-09519-5_52
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/3-540-12868-9_99 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030833923
117 https://doi.org/10.1007/3-540-12868-9_99
118 rdf:type schema:CreativeWork
119 sg:pub.10.1007/3-540-45539-6_27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000285811
120 https://doi.org/10.1007/3-540-45539-6_27
121 rdf:type schema:CreativeWork
122 sg:pub.10.1007/978-3-540-74735-2_31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010365111
123 https://doi.org/10.1007/978-3-540-74735-2_31
124 rdf:type schema:CreativeWork
125 sg:pub.10.1007/978-3-642-21969-6_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028053137
126 https://doi.org/10.1007/978-3-642-21969-6_5
127 rdf:type schema:CreativeWork
128 sg:pub.10.1007/978-3-642-35999-6_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021725223
129 https://doi.org/10.1007/978-3-642-35999-6_2
130 rdf:type schema:CreativeWork
131 sg:pub.10.1007/s00145-011-9111-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044237636
132 https://doi.org/10.1007/s00145-011-9111-4
133 rdf:type schema:CreativeWork
134 sg:pub.10.1007/s10623-014-9965-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030052741
135 https://doi.org/10.1007/s10623-014-9965-1
136 rdf:type schema:CreativeWork
137 sg:pub.10.1007/s11424-015-4085-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010484767
138 https://doi.org/10.1007/s11424-015-4085-1
139 rdf:type schema:CreativeWork
140 sg:pub.10.1007/s11786-009-0016-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047994766
141 https://doi.org/10.1007/s11786-009-0016-7
142 rdf:type schema:CreativeWork
143 https://doi.org/10.1016/j.ffa.2016.06.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012244299
144 rdf:type schema:CreativeWork
145 https://doi.org/10.1016/j.jsc.2010.06.013 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026421537
146 rdf:type schema:CreativeWork
147 https://doi.org/10.1016/j.jsc.2010.06.019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001338627
148 rdf:type schema:CreativeWork
149 https://doi.org/10.1016/j.jsc.2011.05.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012340184
150 rdf:type schema:CreativeWork
151 https://doi.org/10.1016/j.jsc.2011.12.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017103940
152 rdf:type schema:CreativeWork
153 https://doi.org/10.1016/j.jsc.2013.08.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033298909
154 rdf:type schema:CreativeWork
155 https://doi.org/10.1016/s0022-4049(99)00005-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040947089
156 rdf:type schema:CreativeWork
157 https://doi.org/10.1090/mcom/2969 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059342770
158 rdf:type schema:CreativeWork
159 https://doi.org/10.1145/1576702.1576725 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002499019
160 rdf:type schema:CreativeWork
161 https://doi.org/10.1145/1837210.1837225 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032330834
162 rdf:type schema:CreativeWork
163 https://doi.org/10.1145/1837934.1837944 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042071596
164 rdf:type schema:CreativeWork
165 https://doi.org/10.1145/1993886.1993936 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048552226
166 rdf:type schema:CreativeWork
167 https://doi.org/10.1145/2442829.2442860 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017577577
168 rdf:type schema:CreativeWork
169 https://doi.org/10.1145/2442829.2442879 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033894307
170 rdf:type schema:CreativeWork
171 https://doi.org/10.1145/2465506.2465522 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005299081
172 rdf:type schema:CreativeWork
173 https://doi.org/10.1145/2930889.2930914 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001702028
174 rdf:type schema:CreativeWork
175 https://doi.org/10.1145/780506.780516 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007436250
176 rdf:type schema:CreativeWork
177 https://www.grid.ac/institutes/grid.410726.6 schema:alternateName University of Chinese Academy of Sciences
178 schema:name KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100090, Beijing, China
179 SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China
180 School of Cyber Security, University of Chinese Academy of Sciences, 100190, Beijing, China
181 School of Mathematical Sciences, University of Chinese Academy of Sciences, 100190, Beijing, China
182 rdf:type schema:Organization
183 https://www.grid.ac/institutes/grid.458480.5 schema:alternateName Institute of Information Engineering
184 schema:name SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China
185 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...