In the online minimum spanning tree problem, a graph is revealed vertex by vertex; together with every vertex, all edges to vertices that are already known are given, and an online algorithm must irrevocably choose a subset of them as a part of its solution. The advice complexity of an online problem is a means to quantify the information that needs to be extracted from the input to achieve good results. For a graph of size n, we show an asymptotically tight bound of Θ(n log n) on the number of advice bits to produce an optimal solution for any given graph. For particular graph classes, e.g., with bounded degree or a restricted edge weight function, we prove that the upper bound can be drastically reduced; e.g., 5(n − 1) advice bits allow to compute an optimal result if the weight function is the Euclidean distance; if the graph is complete, even a logarithmic number suffices. Some of these results make use of the optimality of Kruskal’s algorithm for the offline setting. We also study the trade-off between the number of advice bits and the achievable competitive ratio. To this end, we perform a reduction from another online problem to obtain a linear lower bound on the advice complexity for any near-optimal solution. Using our results from the advice complexity finally allows us to give a lower bound on the expected competitive ratio of any randomized online algorithm for the problem.
Online minimum spanning tree with advice / M.P. Bianchi, H. Böckenhauer, T. Brülisauer, D. Komm, B. Palano - In: SOFSEM 2016: Theory and Practice of Computer Science / [a cura di] R.M. Freivalds, G. Engels, B. Catania. - [s.l] : Springer Verlag, 2016. - ISBN 9783662491911. - pp. 195-207 (( Intervento presentato al 42. convegno International Conference on Current Trends in Theory and Practice of Computer Science tenutosi a Harrachov nel 2016.
|Titolo:||Online minimum spanning tree with advice|
BIANCHI, MARIA PAOLA (Corresponding)
PALANO, BEATRICE SANTA (Ultimo)
|Parole Chiave:||Computer Science (all); Theoretical Computer Science|
|Settore Scientifico Disciplinare:||Settore INF/01 - Informatica|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/978-3-662-49192-8_16|
|Tipologia:||Book Part (author)|
|Appare nelle tipologie:||03 - Contributo in volume|