In this paper, we present an algorithm called FOARS for obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction. FOARS applies a top-down approach which first partitions the set of pins into several subsets uncluttered by obstacles. Then an obstacle-avoiding Steiner tree is generated for each subset by an obstacle aware version of the rectilinear Steiner minimal tree (RSMT) alg...

BACKGROUND We tested the hypothesis that the shape of the shock waveform affects not only the defibrillation threshold but also the amount of cardiac damage. METHODS AND RESULTS Defibrillation thresholds were determined for 11 waveforms-3 ascending-ramp waveforms, 3 descending-ramp waveforms, 3 rectilinear first-phase biphasic waveforms, a Gurvich waveform, and a truncated exponential biphasi...

Background—We tested the hypothesis that the shape of the shock waveform affects not only the defibrillation threshold but also the amount of cardiac damage. Methods and Results—Defibrillation thresholds were determined for 11 waveforms—3 ascending-ramp waveforms, 3 descending-ramp waveforms, 3 rectilinear first-phase biphasic waveforms, a Gurvich waveform, and a truncated exponential biphasic ...

A directed graph is said to be upward planar if it can be draw in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is said to be rectilinear planar if it can be draw in the plane such that every edge is a horizontal or vertical segment, and no two edges cross. Testing upward planarity and rectilinear planar...

In this paper, we deal with arbitrary convex and concave rectilinear module packing using the Transitive Closure Graph (TCG) representation. The geometric meanings of modules are transparent to TCG as well as its induced operations, which makes TCG an ideal representation for floorplanning/placement with arbitrary rectilinear modules. We first partition a rectilinear module into a set of submod...

A new approximation heuristic for finding a rectilinear Steiner tree of a set of nodes is presented. It starts with a rectilinear minimum spanning tree of the nodes and repeatedly connects a node to the nearest point on the rectangular layout of an edge, removing the longest edge of the loop thus formed. A simple implementation of the heuristic using conventional data structures is compared wit...

We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the “confluent” context in which the routes to exits remain fixed over time, and the “non-confluent” context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allo...

We present e cient algorithms for two problems of facility location. In both problems we want to optimize the location of two facilities with respect to n given sites. The rst problem, the continuous version, has no restrictions for facility locations but in the second one, the discrete version, facilities are chosen from a speci ed set of possible locations. We consider the rectilinear metric ...