Instant fuzzy search is important developing technique from which users can find results character by character with better search experiences. The results must have high speed, good relevancy score and also good ranking functions used to get top results. Many functions are used to consider proximity of keywords which ultimately gives good relevancy score. In this paper, proximity information is used to ranking query results with which gives good time and space complexities. Many previously proposed techniques are used to achieve proximity ranking into instant fuzzy search. Most of the techniques firstly compute results and rank then according to some ranking functions, but if the dataset used is large then it takes time to compute all results and its very time consuming. At this state early termination technique is used to minimize space and time complexity. In this paper, incremental computation algorithm is used to overcome all drawbacks of previous systems and compute relevant results. Also query logs are used which are very useful for most of query suggestion systems, which ultimately reduces time complexity efficiently. The experimental results are computed to show space, time complexity and quality of results.