k-means is one of the most widely used partition based clustering algorithm. But the initial centroids generated randomly by the k-means algorithm cause the algorithm to converge at the local optimum. So to make k-means algorithm globally optimum, the initial centroids must be selected carefully rather than randomly. Though many researchers have already been carried out for the enhancement of k-means algorithm, they have their own limitations. In this paper a new method to formulate the initial centroids is proposed which results in better clusters equally for uniform and non-uniform data sets.

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Distributed algorithms for shortest-path problems are important in the context of routing in computer communication networks. We present a protocol that maintains the shortest-path routes in a dynamic topology, that is, in an environment where links and nodes can fail and recover at arbitrary times. The novelty of this protocol is that it avoids the bouncing effect and the looping problem that occur in the previous approaches of the distributed implementation of Bellman-Ford algorithm. The bouncing effect refers to the very long duration for convergence when failures happen or weights increase, and the nonterminating exchanges of messages, or counting-to-infinity behavior, in disconnected components of the network resulting from failures. The looping problems cause data packets to circulate and, thus, waste bandwidth. These undesirable effects are avoided without any increase in the overall message complexity of previous approaches required in the connected part of the network. The time complexity is better than the distributed Bellman-Ford algorithm encountering failures. The key idea in the implementation is to maintain only loop-free paths, and search for the shortest path only from this set.

We present a distributed protocol for updating and maintaining a minimum-weight spanning tree (MST) in a network with changing topology. The protocol can respond to multiple link/node failures and recoveries that can occur at arbitrary times. Given that an arbitrary finite number of topological changes occur during a period, the protocol finds the MST corresponding to the latest network, within finite time after the last change. The message complexity of the protocol is O(+l+klW h w en k link recoveries and m link failures occur, where IV1 and [El are the total number of nodes and links, respectively.