Global query execution in a multidatabase system can be done parallelly, as all the local databases are independent. In this paper, a cost model that considers parallel execution of subqueries for a global query is developed. In order to obtain maximum parallelism in query execution, it is required to find a query execution plan that is represented in the form of a bushy tree and this query tree should be balanced to the maximal possible extent with respect to execution time. A new bottom up approach called Agglomerative Approach (AA) is proposed to construct balanced bushy trees with respect to execution time. By the deterministic nature of this approach, it generates local optimal solutions. This local minima problem will be severe in the case of graph queries, i.e., queries that are represented with a graph structure. A Simulated annealing Approach (SA) is employed to obtain a (near) optimal solution. These approaches (AA and SA) are suitable for handling on-line and off-line queries respectively. A Hybrid Approach (HA), that is an integration of AA and SA, is proposed to optimize queries for which the estimated time to be spent on optimization is known a priori. Results obtained with AA and SA on both tree and graph structured queries are presented.