Topology Control of Multihop Wireless Networks Using Transmit

Power Adjustment

Paper By: Ram Ramanathan, Regina Resales-Hain

Instructor: Dr Yingshu LiPresented By: R. Jayampathi Sampath

Outline

lNTRODUCTION

PROBLEM STATEMENT

STATIC NETWORKS: OPTIMUM CENTRALIZED ALGORITHMSCONNECTSeparation Edges and VerticesBiconnected GraphBICONN-AUGMENT

MOBILE NETWORKS : DISTRIBUTED HEURISTICSLINT DescriptionLILT 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, noisecontrollable 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 capacityIncrease the end-to-end packet delayDecrease the robustness to node failures

Example 1 – Too sparse networkA danger of network partitioningHigh end to end delays

Example 2 – Dense networkMany nodes interfere with each otherRecompute 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 number

power assigned

d(s)

step number

distance

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 VerticesDefinitions

Let G be a connected graphA separation edge of G is an edge whose removal disconnects GA separation vertex of G is a vertex whose removal disconnects G

ApplicationsSeparation edges and vertices represent single points of failure in a network and are critical to the operation of the network

Example3, 5 and 6 are separation vertices(3,5) is a separation edge

6

2 3

1

5 8

74

Biconnected GraphEquivalent definitions of a bi-connected graph G

Graph G has no separation edges and no separation verticesFor 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

6

2 3

1

5 8

74

Algorithm BICONN-AUGMENTIdentify the bi-connected components in the graph induced by the power assignment from algorithm CONNETThis is done using method based on depth-first searchNode pairs are selected in non-decreasing order of their mutual distance and joined only if they are in different bi- connected componentsThis 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.

Implementation40 nodes spread out with a density of 2 nodes/sq mile

MOBILE NETWORKS : DISTRIBUTED HEURISTICS

The topology is continually changingSolution: 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 heuristicsLocal Information No Topology (LINT)Local Information Link-State Topology (LILT)

Zero overhead protocols; they do not use any special control messages for their operation

LINTUses locally available information colleted by a routing protocolAttempt to keep degree of each node bounded.if d(Ni)>dh

reduce transmit powerif d(Ni)<dl

increase transmit powerdh High threshold on the node degree

dl Low threshold on the node degreeNew power

LILTsignificant 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 partsNeighbor reduction protocol (NRP)

LINT mechanismNeighbor 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 better BICONN uses more power

EXPERIMENTAL RESULTS (Cont.)

LINT is better No significant changes