Telvis Calhoun CS 8980-05 – Dr. Li – 11/13/2008

1. Disjoint Multipath Routing to two distinct drains in a multi-drain sensor networkPreethaThulasiraman, SrinivasanRamasubramanianand MarwanKrunz Telvis Calhoun CS 8980-05 – Dr. Li – 11/13/2008

2. Overview • Motivation • Authors present a multipath routing technique with minimal time complexity and messaging complexity. • Experiment • Authors compare new technique against an existing algorithm within a simulated environment containing up to 300 nodes. • Conclusions • The technique reduces average path length to a drain • The technique reduces overall complexity

3. Multipath Routing • Multipath routing decreases average path length to a drain (sink). • Reducing energy cost of forwarding data. • Calculating multipath routes is expensive. • Forwarding MPR packets requires large forwarding tables or message size. • Authors use colored trees to minimize the complexity.

4. Colored Tree • Construct red and blue tree rooted at distinct drains. • Each node has a next hop for each tree. • Routing performed based on the link thus requiring no lookup. Single Drain Network Two Drain Network

5. Disjoint Path Multi-Drain Problem (DRMD-2) • Identify D trees each rooted at a distinct drain. • Each node has 2 node disjoint paths to two drains. • Algorithm • Construct G’ from G adding virtual drain (v) with |D| links between v and drains. • Route using tree pairs. Drain address + 1-bit to identify tree used to forward packets. • Each node is associated with a single tree. This requires a node to use a single drain on red and blue trees. Tree where the paths for all nodes traverse drain d3. Tree where the paths traverse either d1 or d2. Network with virtual drain

6. Colored Tree Multiple Pair Problem (CTMP) • There exists a tree-pair for every node where two paths to primary and one path to secondary that are node-disjoint. • Bits required log D. Route table entries are 2 * D.

7. Integer Linear Program • Uses auxiliary graphs for each drain using virtual nodes (p,s) • Virtual drain v that is connected to p and s virtual nodes of every aux graph.

8. Distributed Algorithm for CTMP • 3 steps: • Distributed depth first search (DFS) numbering of the nodes. • Distributed path augmentation for computing the two trees. • Choosing aux path that minimizes the sum of the two path lengths. • Generalized low-point. The low-point path of a node n is ni[1]i[2]…i[k]n’ (k>=0) • Node n is the DFS parent of of node i1 • Node i[j-1] is DFS-parent of ij • DFS-index of n’ is lower than • DFS-index of n’ is lowest among all possible lengths.

9. DFS Numbering • Number drains 1 through D. Highest number drain initiates node numbering. • Compute generalized low point value (GLPV) and generalized low point neighbor (GLPN). • Construct low point table containing low point paths to each drain.

10. Distributed Path Augmentation • Arrange the neighbors in the neighbor list in increasing order of their DFS-indices. • On receiving a TOKEN message, initiate path search for each neighbor. • Every node forwards SEARCH message to every neighbor according to some rules. Flag nodes belonging to augmented path. • Forward TOKEN to flagged nodes in a reverse traversal. • Receive RETURN from all neighbors and then send RETURN to the parent node.

11. Auxiliary Graph Selection • Nodes choose the auxiliary graph that provides the minimum sum of the primary and secondary paths. • Forwarded paths contain primary drain address and bit. • 0 indicates the packet is transmitted over the tree to the primary drain. • 1 indicates the packet is transmitted over the tree to one of the secondary drains.

12. Example (a) Primary tree rooted at drain d3; (b) Secondary tree rooted at either drains d2 or d1; (c) Primary tree rooted at drain d2; (d) Secondary tree rooted at drains d3 or d1; (e) Primary tree rooted at drain d1; and (f) Secondary tree rooted at drains d3 or d2.

13. Complexity of Distributed Algorithm • Numbering phase • O(L) • Augmentation phase • Each drain performs augmentation in parallel so complexity is O(L) and message complexity is O(D*L) • Graph selection is O(D)

14. Experiment • Compare performance to solution obtained by ILP using CPLEX 8.0 solver. • ILP modeled using 20, 30, 40 and 50 nodes network with 3 drains. • Evaluated distributed algorithm using random topologies of 50, 100, 200 and 300 nodes that employ 3,4 and 5 drains. • More drains reduces average path length by 46.2% for CTMP problem. 7.53->4.05 • Disjoint routing to distinct drains significantly outperforms disjoint routing to the same drain. • Simulation with links of unequal costs. 10 random topologies for each scenario. Performance similar to those with equal costs.

15. Conclusion • Authors present a multipath routing technique with minimal time complexity and messaging complexity. • Authors compare distributed CTMP solution against ILP within a simulated environment containing up to 300 nodes. • Distributed technique reduces average path length to a drain • Distributed technique reduces overall complexity

16. References • Thulasiraman, P.; Ramasubramanian, S.; Krunz, M., "Disjoint Multipath Routing to Two Distinct Drains in a Multi-Drain Sensor Network," INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE , vol., no., pp.643-651, 6-12 May 2007