Searching networks with unrestricted edge costs

Best-first and depth-first heuristic search algorithms often assume underlying search graphs with only nonnegative edge costs and attempt to optimize simple objective functions. Applicability of these algorithms to graphs with both positive and negative edge costs is not completely studied. In the paper, two new problems are identified: one in computational geometry and the other in the layout design of very large scale integrated (VLSI) circuits. The former problem relates to a weight-balanced bipartitioning of a given set of points in a plane. The goal of the second problem is to find an area-balanced staircase path in a VLSI floorplan. Formulations of these problems lead to an interesting directed acyclic search graph with positive, zero and negative edge costs and an objective function of general nature. These problems are NP-hard. To solve such general problems optimally, search schemes are proposed. Experimental results reveal the efficacy and versatility of the proposed schemes, the depth-first scheme being the better choice. It is shown that the classical number-partitioning problem can also be formulated in this framework