Replica Placement on Directed Acyclic Graphs

The replica placement problem has been well studied on trees. In this paper, we study this problem on directed acyclic graphs. The replica placement problem on general DAGs generalizes the set cover problem. We present a constant factor approximation algorithm for the special case of DAGs having bounded degree and bounded tree-width (BDBT-DAGs). We also present a constant factor approximation algorithm for DAGs composed of local BDBT-DAGs connected in a tree like manner (TBDBT-DAGs). The latter class of DAGs generalizes trees as well; we improve upon the previously best known approximation ratio for the problem on trees. Our algorithms are based on the LP rounding technique; the core component of our algorithm exploits the structural properties of tree-decompositions to massage the LP solution into an integral solution.

[1]  Paul Renaud-Goud,et al.  Optimal Algorithms and Approximation Algorithms for Replica Placement with Distance Constraints in Tree Networks , 2012, 2012 IEEE 26th International Parallel and Distributed Processing Symposium.

[2]  Samir Khuller,et al.  Set Cover Revisited: Hypergraph Cover with Hard Capacities , 2012, ICALP.

[3]  Yi-Fang Lin,et al.  Optimal placement of replicas in data grid environments with locality assurance , 2006, 12th International Conference on Parallel and Distributed Systems - (ICPADS'06).

[4]  Yi-Fang Lin,et al.  Optimal replica placement in hierarchical Data Grids with locality assurance , 2008, J. Parallel Distributed Comput..

[5]  Yves Robert,et al.  Replica Placement and Access Policies in Tree Networks , 2008, IEEE Transactions on Parallel and Distributed Systems.

[6]  D. T. Lee,et al.  Capacitated Domination Problem , 2007, Algorithmica.

[7]  Rajiv Gandhi,et al.  An improved approximation algorithm for vertex cover with hard capacities , 2003, J. Comput. Syst. Sci..

[8]  Konstantinos Kalpakis,et al.  Optimal Placement of Replicas in Trees with Read, Write, and Storage Costs , 2001, IEEE Trans. Parallel Distributed Syst..

[9]  Joseph Naor,et al.  Covering problems with hard capacities , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[10]  Laurence A. Wolsey,et al.  An analysis of the greedy algorithm for the submodular set covering problem , 1982, Comb..

[11]  Shay Kutten,et al.  Optimal allocation of electronic content , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[12]  Yogish Sabharwal,et al.  Replica Placement via Capacitated Vertex Cover , 2013, FSTTCS.