Related papers: Compact Floor-Planning via Orderly Spanning Trees
In this paper, we consider the problem of determining in polynomial time whether a given planar point set $P$ of $n$ points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing $P$, and present…
Floorplanning determines the shapes and locations of modules on a chip canvas and plays a critical role in optimizing the chip's Power, Performance, and Area (PPA) metrics. However, existing floorplanning approaches often fail to integrate…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
With the increase in the complexity of chip designs, VLSI physical design has become a time-consuming task, which is an iterative design process. Power planning is that part of the floorplanning in VLSI physical design where power grid…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
Given a set of rectangular modules with fixed area and variable dimensions, and a fixed rectangular circuit. The placement of Fixed-Outline Floorplanning with Soft Modules (FOFSM) aims to determine the dimensions and position of each module…
We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
In this paper, we establish two necessary conditions for a joint triangulation of two sets of $n$ points in the plane and conjecture that they are sufficient. We show that these necessary conditions can be tested in $O(n^3)$ time. For the…
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…
Autonomous navigation of ground robots has been widely used in indoor structured 2D environments, but there are still many challenges in outdoor 3D unstructured environments, especially in rough, uneven terrains. This paper proposed a…
Network-on-chip (NoC) architectures have been proposed as a promising alternative to classical bus-based communication architectures. In this paper, we propose a two phases framework to solve application-specific NoCs topology generation…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Given a set of $n$ points $S$ in the plane, a triangulation $T$ of $S$ is a maximal set of non-crossing segments with endpoints in $S$. We present an algorithm that computes the number of triangulations on a given set of $n$ points in time…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
Given an $n$-vertex planar embedded digraph $G$ with non-negative edge weights and a face $f$ of $G$, Klein presented a data structure with $O(n\log n)$ space and preprocessing time which can answer any query $(u,v)$ for the shortest path…
Let G be a plane graph of n nodes, m edges, f faces, and no self-loop. G need not be connected or simple (i.e., free of multiple edges). We give three sets of coding schemes for G which all take O(m+n) time for encoding and decoding. Our…
The adoption of machine learning-based techniques for analog integrated circuit layout, unlike its digital counterpart, has been limited by the stringent requirements imposed by electric and problem-specific constraints, along with the…
Maps --- specifically floor plans --- are useful for a variety of tasks from arranging furniture to designating conceptual or functional spaces (e.g., kitchen, walkway). We present a simple algorithm for quickly laying a floor plan (or…