Advances in Greedy Algorithms 254 threshold. The stable path MANET routing protocols are distributed and on-demand in nature and thus are not guaranteed to determine the most stable routes (Meghanathan 2006d; Meghanathan 2007) . Stability is an important design criterion to be considered while developing multi-hop MANET routing protocols. The commonly used route discovery approach of flooding the route request can easily lead to congestion and also consume node battery power. Frequent route

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... ges can also result in out-of-order data packet delivery, causing high jitter in multimedia, real-time applications. In the case of reliable data transfer applications, failure to receive an acknowledgement packet within a particular timeout interval can also trigger retransmissions at the source side. As a result, the application layer at the receiver side might be overloaded in handling out-of-order, lost and duplicate packets, leading to reduced throughput. Thus, stability is also important from quality of service (QoS) point of view too. This chapter addresses the issue of finding the sequence of stable paths and trees, such that the number of path and tree transitions is the global minimum. In the first half of the chapter, we present an algorithm called OptPathTrans (Meghanathan & Farago, 2005) to determine the sequence of stable paths for a source-destination (s-d) communication session. Given the complete knowledge of the future topology changes, the algorithm operates on the greedy "look-ahead" principle: Whenever an s-d path is required at a time instant t, choose the longest-living s-d path from t. The sequence of long-living stable paths obtained by applying the above strategy for the duration of the s-d session is called the stable mobile path and it incurs the minimum number of route transitions. We quantify route stability in terms of the number of route transitions. Lower the number of route transitions, higher is the stability of the routing algorithm. In the second half of the chapter, we show that the greedy look-ahead principle behind OptPathTrans is very general and can be extended to find a stable sequence of any communication structure as long as there is an underlying algorithm or heuristic to determine that particular communication structure. In this direction, we propose algorithm OptTreeTrans (Meghanathan, 2006c) to determine the sequence of stable multicast Steiner trees for a multicast session. The problem of determining the multicast Steiner tree is that given a weighted network graph G = (V, E) where V is the set of vertices, E is the set of edges connecting these vertices and S, is a subset of set of vertices V, called the multicast group or Steiner points, we want to determine the set of edges of G that can connect all the vertices of S and they form a tree. It is very rare that greedy strategies give an optimal solution. Algorithms OptPathTrans and OptTreeTrans join the league of Dijkstra algorithm, Minimum spanning tree Kruskal and Prim algorithms (Cormen et. al., 2001 ) that have used greedy strategies, but yet give optimal solution. In another related work, we have also proposed an algorithm to determine the sequence of stable connected dominating sets for a network session (Meghanathan, 2006b) . The performance of algorithms OptPathTrans and OptTreeTrans have been studied using extensive simulations under two different scenarios: (1) Scenarios in which the complete knowledge of the future topology changes is available at the time of path/tree selection and (2) Scenarios in which the locations of nodes are only predicted for the near future and not exact. To simulate the second scenario, we consider a location prediction model called "Prediction with Uncertainty" that predicts the future locations of nodes at different time instants based on the current location, velocity and direction of travel of each node, even though we are not certain of the velocity and direction of travel in the future. Simulation