Interconnect design has emerged as one of the major challenges facing chip designers as VLSI manufacturing progresses and gate sizes scale down. Dynamic programming (DP) is an efficient and robust technique for finding optimal solutions to interconnect optimization problems in VLSI design. However, DP's huge memory requirement often limits its effectiveness and sometimes, due to limited storage resources, even makes it impossible to solve a problem of practical size. Since interconnect optimization is often a subprocess embedded in an upper level design procedure, a memory and time efficient implementation of DP can be very favorable to circuit designers. In this paper, we develop a new memory-efficient dynamic programming approach to interconnect optimization problems. Our method utilizes selective storage and recomputation technique. This memory and time efficient algorithm speeds up the dynamic programming method without compromising solution quality. Experiments show tremendous saving, both in storage and time, over traditional dynamic programming algorithms. Our novel approach can also be generalized for other VLSI applications using DP algorithms.