Actualités
  Période
semaine
ou mois
aucune période


  Thèmes:
Thèses
Colloques
Autres
Groupes
Tous les thèmes

   
  Liens:
Voir les thèses

Voir les colloques

Voir les autres événements

Voir la page des groupes

Accéder à l'intranet

Intitulé:   
Improved approximability and non-approximability results for graph diameter decreasing problems
du groupe GT Graphes et Applications

Date 2010-09-10  14:00-15:00
TitreImproved approximability and non-approximability results for graph diameter decreasing problems 
RésuméWe study two variants of the problem of adding edges to a graph so as to reduce the resulting diameter. More precisely, given a graph G = (V, E), and two positive integers D and B, the Minimum-Cardinality Bounded-Diameter Edge Addition (MCBD) problem is to find a minimum cardinality set F of edges to be added to G in such a way that the diameter of G+F is less than or equal to D, while the Bounded-Cardinality Minimum-Diameter Edge Addition (BCMD) problem is to find a set F of B edges to be added to G in such a way that the diameter of G + F is minimized. Both problems are well known to be NP-hard, as well as approximable within O(log n log D) and 4 (up to an additive term of 2), respectively. In this paper, we improve these long-standing approximation ratios to O(log n) and to 2 (up to an additive term of 2), respectively. As a consequence, we close, in an asymptotic sense, the gap on the approximability of the MCBD problem, which was known to be not approximable within c log n, for some constant c > 0, unless P = NP. Remarkably, as we further show in the paper, our approximation ratio remains asymptotically tight even if we allow for a solution 5 whose diameter is optimal up to a multiplicative factor approaching 3. On the other hand, on the positive side, we show that at most twice of the minimal number of additional edges suffices to get at most twice of the required diameter.  
LieuSalle 178 
OrateurDavide Bilo 
UrlUniversité de L'Aquila 



Aucun document lié à cet événement.

Retour
Retour à l'index