Although distributed computing over a network of computers has become a reality, its success mainly depends on the performance of the underlying network. In this paper, we consider the problem of designing a local area network with specified cost and performance constraints. The cost and performance of a local area network (LAN) are directly related to its topology. Using the a priori knowledge of the approximate number of users of the network and the kind of communication traffic that must be supported, the designer can optimize the design of the of a LAN for superior performance. Design decisions include the number of LAN segments, number of bridges, assignment of users to segments, and the method to interconnect the segments through bridges. In case of ATM networks, the decisions are regarding the number of ATM switches, the assignment of hosts to switches, and the way to connect switches through cross-connects. While assigning too many users to the same segment may cause large delays due to the sharing of network bandwidth, splitting the LAN into too many segments will increase the cost of the LAN. We report a greedy heuristic algorithm for Local Area Network Design. We propose an interesting method to construct good initial solutions to the topology design problem using a heuristic method which is based on the three-opt technique for solving the travelling salesperson problem. Our experimental results indicate that the heuristic algorithm finds good solutions.Unlike a multiprocessor, a distributed computing environment grows or shrinks dynamically. The number of users may grow way beyond the number for which the network was originally designed, resulting in a performance * Dilip and Anubhav were M.Tech students of Computer Technology in the Department of Electrical Engineering when this work was carried out. An equipment grant from Sun Microsystems is gratefully acknowledged.degradation. In such a situation, a complete redegin of the network may not be feasible without incurring a prolonged disruption in service and a significant rewiring cost. What is desirable is an incremental redesign, which preserves most features of the existing network and requires as little rewiring as possible. We consider the problem of network redesign as an optimisation problem and present heuristic algorithms for the problem. The algorithm works in four phases which correspond to four network redesign options that are progressively more expensive. Thus, while the first phase tries to achieve better network performance by user reassignment, the fourth phase calls for creation of an additional LAN segment using an additional bridge. Our heuristic algorithm is greedy in that it chooses a more expensive redesign technique only when the more economical ones fail to provide the desired performance. We present experimental results of an implementation of our redesign heuristic.