Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of $n$ vertices and $h$ holes. We introduce a \emph{graph of oriented distances} to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in $\min \{\,O(n^\omega), O(n^2 + nh \log h + \chi^2)\,\}$ time, where $\omega<2.373$ denotes the matrix multiplication exponent and $\chi\in \Omega(n)\cap O(n^2)$ is the number of edges of the graph of oriented distances. We also provide a faster algorithm for computing the diameter that runs in $O(n^2 \log n)$ time

Path Planning with Modified a Star Algorithm for a Mobile Robot

AbstractThis article deals with path planning of a mobile robot based on a grid map. Essential assumption for path planning is a mobile robot with functional and reliable reactive navigation and SLAM. Therefore, such issues are not addressed in this article. The main body of the article introduces several modifications (Basic Theta*, Phi*) and improvements (RSR, JPS) of A star algorithm. These modifications are focused primarily on computational time and the path optimality. Individual modifications were evaluated in several scenarios, which varied in the complexity of environment. On the basis of these evaluations, it is possible to choose path planning method suitable for individual scenario

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster

Shortest Paths and Steiner Trees in VLSI Routing

Routing is one of the major steps in very-large-scale integration (VLSI) design. Its task is to find disjoint wire connections between sets of points on a chip, subject to numerous constraints. This problem is solved in a two-stage approach, which consists of so-called global and detailed routing steps. For each set of metal components to be connected, global routing reduces the search space by computing corridors in which detailed routing sequentially determines the desired connections as shortest paths. In this thesis, we present new theoretical results on Steiner trees and shortest paths, the two main mathematical concepts in routing. In the practical part, we give computational results of BonnRoute, a VLSI routing tool developed at the Research Institute for Discrete Mathematics at the University of Bonn. Interconnect signal delays are becoming increasingly important in modern chip designs. Therefore, the length of paths or direct delay measures should be taken into account when constructing rectilinear Steiner trees. We consider the problem of finding a rectilinear Steiner minimum tree (RSMT) that --- as a secondary objective --- minimizes a signal delay related objective. Given a source we derive some structural properties of RSMTs for which the weighted sum of path lengths from the source to the other terminals is minimized. Also, we present an exact algorithm for constructing RSMTs with weighted sum of path lengths as secondary objective, and a heuristic for various secondary objectives. Computational results for industrial designs are presented. We further consider the problem of finding a shortest rectilinear Steiner tree in the plane in the presence of rectilinear obstacles. The Steiner tree is allowed to run over obstacles; however, if it intersects an obstacle, then no connected component of the induced subtree must be longer than a given fixed length. This kind of length restriction is motivated by its application in VLSI routing where a large Steiner tree requires the insertion of repeaters which must not be placed on top of obstacles. We show that there are optimal length-restricted Steiner trees with a special structure. In particular, we prove that a certain graph (called augmented Hanan grid) always contains an optimal solution. Based on this structural result, we give an approximation scheme for the special case that all obstacles are of rectangular shape or are represented by at most a constant number of edges. Turning to the shortest paths problem, we present a new generic framework for Dijkstra's algorithm for finding shortest paths in digraphs with non-negative integral edge lengths. Instead of labeling individual vertices, we label subgraphs which partition the given graph. Much better running times can be achieved if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy. As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, the algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goal-oriented techniques leads to considerably reduced running time. We illustrate this with the routing program BonnRoute on leading-edge industrial chips. Finally, we present computational results of BonnRoute obtained on real-world VLSI chips. BonnRoute fulfills all requirements of modern VLSI routing and has been used by IBM and its customers over many years to produce more than one thousand different chips. To demonstrate the strength of BonnRoute as a state-of-the-art industrial routing tool, we show that it performs excellently on all traditional quality measures such as wire length and number of vias, but also on further criteria of equal importance in the every-day work of the designer

Geometric shortest path containers [online]

In this paper, we consider Dijkstra\u27s algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for on-line queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge. Based on these geometric objects, the search space for on-line computation can be reduced significantly. Shortest path queries can then be answered by Dijkstra\u27s algorithm restricted to edges where the corresponding geometric object contains the target. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are real-world traffic networks, the typical field of application for this scenario. Furthermore, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths. Finally, we present a software framework in C++ to realize the implementations of all of our variants of Dijkstra\u27s algorithm. A basic implementation of the algorithm is refined for each modification and - even more importantly - these modifications can be combined in any possible way without loss of efficiency

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Simulation of autonomous UAV navigation with collision avoidance and spatial awareness.

The goal of this thesis is to design a collision-free autonomous UAV navigation system with spatial awareness ability within a comprehensive simulation framework. The navigation system is required to find a collision-free trajectory to a randomly assigned 3D target location without any prior map information. The implemented navigation system contains four main components: mapping, localisation, cognition and control system, where the cognition system makes execution command based on the perceived position information about obstacles and UAV itself from mapping and localisation system respectively. The control system is responsible for executing the input command made from the cognition system. The implementation for the cognition system is split into three case studies for real-life scenarios, which are restricted area avoidance, static obstacle avoidance and dynamic obstacles. The experiment results in the three cases have been conducted, and the UAV is capable of determining a collision-free trajectory under all three cases of environments. All simulated components were designed to be analogous to their real-world counterpart. Ideally, the simulated navigation framework can be transferred to a real UAV without any changes. The simulation framework provides a platform for future robotic research. As it is implemented in a modular way, it is easier to debug. Hence, the system has good reliability. Moreover, the system has good readability, maintainability and extendability.PhD in Manufacturin

De Novo Protein Structure Modeling and Energy Function Design

The two major challenges in protein structure prediction problems are (1) the lack of an accurate energy function and (2) the lack of an efficient search algorithm. A protein energy function accurately describing the interaction between residues is able to supervise the optimization of a protein conformation, as well as select native or native-like structures from numerous possible conformations. An efficient search algorithm must be able to reduce a conformational space to a reasonable size without missing the native conformation. My PhD research studies focused on these two directions. A protein energy function—the distance and orientation dependent energy function of amino acid key blocks (DOKB), containing a distance term, an orientation term, and a highly packed term—was proposed to evaluate the stability of proteins. In this energy function, key blocks of each amino acids were used to represent each residue; a novel reference state was used to normalize block distributions. The dependent relationship between the orientation term and the distance term was revealed, representing the preference of different orientations at different distances between key blocks. Compared with four widely used energy functions using six general benchmark decoy sets, the DOKB appeared to perform very well in recognizing native conformations. Additionally, the highly packed term in the DOKB played its important role in stabilizing protein structures containing highly packed residues. The cluster potential adjusted the reference state of highly packed areas and significantly improved the recognition of the native conformations in the ig_structal data set. The DOKB is not only an alternative protein energy function for protein structure prediction, but it also provides a different view of the interaction between residues. The top-k search algorithm was optimized to be used for proteins containing both α-helices and β-sheets. Secondary structure elements (SSEs) are visible in cryo-electron microscopy (cryo-EM) density maps. Combined with the SSEs predicted in a protein sequence, it is feasible to determine the topologies referring to the order and direction of the SSEs in the cryo-EM density map with respect to the SSEs in the protein sequence. Our group member Dr. Al Nasr proposed the top-k search algorithm, searching the top-k possible topologies for a target protein. It was the most effective algorithm so far. However, this algorithm only works well for pure a-helix proteins due to the complexity of the topologies of β-sheets. Based on the known protein structures in the Protein Data Bank (PDB), we noticed that some topologies in β-sheets had a high preference; on the contrary, some topologies never appeared. The preference of different topologies of β-sheets was introduced into the optimized top-k search algorithm to adjust the edge weight between nodes. Compared with the previous results, this optimization significantly improved the performance of the top-k algorithm in the proteins containing both α-helices and β-sheets