| bibtype |
J -
Journal Article
|
| ARLID |
0545447 |
| utime |
20240103230145.5 |
| mtime |
20210912235959.9 |
| SCOPUS |
85114479243 |
| WOS |
000704053400012 |
| DOI |
10.1016/j.ijar.2021.07.014 |
| title
(primary) (eng) |
The dual polyhedron to the chordal graph polytope and the rebuttal of the chordal graph conjecture |
| specification |
| page_count |
16 s. |
| media_type |
E |
|
| serial |
| ARLID |
cav_un_epca*0256774 |
| ISSN |
0888-613X |
| title
|
International Journal of Approximate Reasoning |
| volume_id |
138 |
| volume |
1 (2021) |
| page_num |
188-203 |
| publisher |
|
|
| keyword |
learning decomposable models |
| keyword |
chordal graph polytope |
| keyword |
clutter inequalities |
| keyword |
dual polyhedron |
| author
(primary) |
| ARLID |
cav_un_auth*0101202 |
| name1 |
Studený |
| name2 |
Milan |
| institution |
UTIA-B |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| full_dept |
Department of Decision Making Theory |
| garant |
K |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0332730 |
| name1 |
Cussens |
| name2 |
J. |
| country |
GB |
|
| author
|
| ARLID |
cav_un_auth*0216188 |
| name1 |
Kratochvíl |
| name2 |
Václav |
| institution |
UTIA-B |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department |
MTR |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| source |
|
| cas_special |
| project |
| project_id |
GA19-04579S |
| agency |
GA ČR |
| country |
CZ |
| ARLID |
cav_un_auth*0380558 |
|
| abstract
(eng) |
The integer linear programming approach to structural learning of decomposable graphical models led us earlier to the concept of a chordal graph polytope. An open mathematical question motivated by this research is what is the minimal set of linear inequalities defining this polytope, i.e. what are its facet-defining inequalities, and we came up in 2016 with a specific conjecture that it is the collection of so-called clutter inequalities. In this theoretical paper we give an implicit characterization of the minimal set of inequalities. Specifically, we introduce a dual polyhedron (to the chordal graph polytope) defined by trivial equality constraints, simple monotonicity inequalities and certain inequalities assigned to incomplete chordal graphs. Our main result is that the vertices of this polyhedron yield the facet-defining inequalities for the chordal graph polytope. We also show that the original conjecture is equivalent to the condition that all vertices of the dual polyhedron are zero-one vectors. Using that result we disprove the original conjecture: we find a vector in the dual polyhedron which is not in the convex hull of zero-one vectors from the dual polyhedron. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2022 |
| num_of_auth |
3 |
| presentation_type |
PR |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0322204 |
| confidential |
S |
| mrcbC86 |
3+4 Article Computer Science Artificial Intelligence |
| mrcbC91 |
C |
| mrcbT16-e |
COMPUTERSCIENCEARTIFICIALINTELLIGENCE |
| mrcbT16-j |
0.721 |
| mrcbT16-s |
1.066 |
| mrcbT16-D |
Q3 |
| mrcbT16-E |
Q2 |
| arlyear |
2021 |
| mrcbU14 |
85114479243 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000704053400012 WOS |
| mrcbU63 |
cav_un_epca*0256774 International Journal of Approximate Reasoning 0888-613X 1873-4731 Roč. 138 č. 1 2021 188 203 Elsevier |
|