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Dynamic programming for graphs on surfaces
dc.contributor.author | Rué Perna, Juan José |
dc.contributor.author | Sau, Ignasi |
dc.contributor.author | Thilikos, Dimitrios |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-05-05T11:09:58Z |
dc.date.available | 2016-05-05T11:09:58Z |
dc.date.issued | 2014-02-01 |
dc.identifier.citation | Rue, J., Sau, I., Thilikos, D. Dynamic programming for graphs on surfaces. "ACM transactions on algorithms", 01 Febrer 2014, vol. 10, núm. 2. |
dc.identifier.issn | 1549-6325 |
dc.identifier.uri | http://hdl.handle.net/2117/86631 |
dc.description.abstract | We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k) · n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called surface cut decomposition, generalizing sphere cut decompositions of planar graphs, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upper-bounded by the number of noncrossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a single-exponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2O(k) · n steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve most previous results in this direction. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Graph Algorithms |
dc.subject.other | analysis of algorithms |
dc.subject.other | parameterized algorithms |
dc.subject.other | graphs on surfaces |
dc.subject.other | branchwidth |
dc.subject.other | dynamic programming |
dc.subject.other | polyhedral embeddings |
dc.subject.other | noncrossing partitions |
dc.title | Dynamic programming for graphs on surfaces |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.identifier.doi | 10.1145/2556952 |
dc.rights.access | Open Access |
local.identifier.drac | 17751774 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/208471/EU/Combinatorial methods, from enumerative topology to random discrete structures and compact data representations./EXPLOREMAPS |
local.citation.author | Rue, J.; Sau, I.; Thilikos, D. |
local.citation.publicationName | ACM transactions on algorithms |
local.citation.volume | 10 |
local.citation.number | 2 |
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