Topology Control of Multihop Wireless Networks Using Transmit Power Adjustment Paper By : Ram Ramanathan, Regina Resales-Hain Instructor : Dr Yingshu Li Presented By : R. Jayampathi Sampath

Outline lNTRODUCTION PROBLEM STATEMENT STATIC NETWORKS: OPTIMUM CENTRALIZED ALGORITHMS CONNECT Separation Edges and Vertices Biconnected Graph BICONN-AUGMENT MOBILE NETWORKS : DISTRIBUTED HEURISTICS LINT Description LILT Description EXPERIMENTAL RESULTS

lNTRODUCTION “Multihop wireless network” a packet may have to traverse multiple consecutive wireless links to reach its destination. “Topology” set of communication links between node pairs used explicitly or implicitly by a routing mechanism. uncontrollable factors: mobility, weather, noise controllable factors: transmit power, antenna direction This paper addresses the problem of controlling the topology of the network by changing the transmit powers of the nodes. Controlling the set of neighbors to which a node talks to is the basic approach.

lNTRODUCTION(Contd.) Why do we need to control the topology? Draw back of a wrong topology Reduce the capacity Increase the end-to-end packet delay Decrease the robustness to node failures Example 1 – Too sparse network A danger of network partitioning High end to end delays Example 2 – Dense network Many nodes interfere with each other Recompute routes even if small node movements

PROBLEM STATEMENT Definition 1: A multihop wireless network is represented as M = (N, L), where N is a set of nodes and L is a set of coordinates on the plane denoting the locations of the nodes. Definition 4: The least-power function gives the minimum power needed to communicate a distance of d. Definition 6: Problem Connected MinMax Power (CMP). Given an M = (N, L), and a least-power function find a per-node minimal assignment of transmit powers such that the induced graph of (M, p) is connected, and is a minimum.

PROBLEM STATEMENT (Contd.) Definition 7: Problem Biconnectivity Augmentation with MinMax Power (BAMP). Given a multihop wireless net M = (N, L), a least-power function and an initial assignment of transmit powers such that the induced graph of (M, p) is connected, find a pernode minimal set of power increases such that the induced graph of is biconnected, and is a minimum.

STATIC NETWORKS: OPTIMUM CENTRALIZED ALGORITHMS s-p step numberpower assigned d(s) step numberdistance

Algorithm CONNECT (Contd.) side-effect edge A side effect edge may form a loop with other edges and may allow the lowering of some power levels and the elimination of some edges added previously.

Separation Edges and Vertices Definitions Let G be a connected graph A separation edge of G is an edge whose removal disconnects G A separation vertex of G is a vertex whose removal disconnects G Applications Separation edges and vertices represent single points of failure in a network and are critical to the operation of the network Example 3, 5 and 6 are separation vertices (3,5) is a separation edge

Biconnected Graph Equivalent definitions of a bi-connected graph G Graph G has no separation edges and no separation vertices For any two vertices u and v of G, there are two disjoint simple paths between u and v (i.e., two simple paths between u and v that share no other vertices or edges) For any two vertices u and v of G, there is a simple cycle containing u and v Example

Algorithm BICONN-AUGMENT Identify the bi-connected components in the graph induced by the power assignment from algorithm CONNET This is done using method based on depth-first search Node pairs are selected in non-decreasing order of their mutual distance and joined only if they are in different bi- connected components This is continued until the network is biconnectd.

STATIC NETWORKS: OPTIMUM CENTRALIZED ALGORITHMS (Contd.) Theorem 1: Algorithm CONNECT is an optimum solution to the CMP problem. Proof: Lines 4, 5 create an edge between two nodes if they are in different clusters. Line 7 ensures that if we end then the graph is connected and line 3 ensures that if we end then all node pairs have been considered. Thus, the algorithm is correct. Theorem 2: Algorithm BICONN-AUGMENT produces an optimum solution to the BAMP problem. Proof: The correctness of BICONN-AUGMENT follows from lines 3 and 4 which force nodes to be in the same bi-connected component. The proofs for optimality and per-node minimality are similar to that for theorem 1.

Implementation 40 nodes spread out with a density of 2 nodes/sq mile

MOBILE NETWORKS : DISTRIBUTED HEURISTICS The topology is continually changing Solution: continually readjust the transmit powers of the nodes to maintain the desired topology. The solution must use only local or already available information. Eg. Positions Centralized solutions not available in a mobile context. Present two distributed heuristics Local Information No Topology (LINT) Local Information Link-State Topology (LILT) Zero overhead protocols; they do not use any special control messages for their operation

LINT Uses locally available information colleted by a routing protocol Attempt to keep degree of each node bounded. if d(N i )>d h reduce transmit power if d(N i )<d l increase transmit power d h High threshold on the node degree d l Low threshold on the node degree New power

LILT significant shortcomings of LINT Unaware of network connectivity Danger of a network partitioning LILT uses global information available in locally to recognize and repair network partitions Two main parts Neighbor reduction protocol (NRP) LINT mechanism Neighbor addition protocol (NAP) Triggered whenever an event driven or periodic link-state updates arrives The purpose triggering is to override the high threshold bounds and increase the power if the topology change indicated by the routing update results in undesirable connectivity.

EXPERIMENTAL RESULTS BICONN betterBICONN uses more power

EXPERIMENTAL RESULTS (Cont.) LINT is betterNo significant changes