Joonsoo Choi

Bio: Joonsoo Choi is an academic researcher from Kookmin University. The author has contributed to research in topics: Euclidean shortest path & Constrained Shortest Path First. The author has an hindex of 7, co-authored 15 publications receiving 244 citations. Previous affiliations of Joonsoo Choi include Courant Institute of Mathematical Sciences.

Approximate Euclidean shortest path in 3-space

Abstract: Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited As this problem is NP-hard, his approach represents an important step towards practical algorithms Unfortunately, there are non-trivial gaps in the original description Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties Among the tools needed are root-separation bounds and non-trivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers

Approximate euclidean shortest paths in 3-space

Abstract: Papadimitriou's approximation approach to the Euclidean shortest path (ESP) in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. However, there are several gaps in the original description. Besides giving a complete treatment in the framework of bit complexity, we also improve on his subdivision method. Among the tools needed are root-separation bounds and nontrivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

Precision-Sensitive Euclidean Shortest Path in 3-Space

Abstract: This paper introduces the concept of precision-sensitive algorithms, analogous to the well-known output-sensitive algorithms. We exploit this idea in studying the complexity of the 3-dimensional Euclidean shortest path problem. Specifically, we analyze an incremental approximation approach and show that this approach yields an asymptotic improvement of running time. By using an optimization technique to improve paths on fixed edge sequences, we modify this algorithm to guarantee a relative error of O(2-r) in a time polynomial in r and $1/\delta$, where $\delta$ denotes the relative difference in path length between the shortest and the second shortest path. Our result is the best possible in some sense: if we have a strongly precision-sensitive algorithm, then we can show that unambiguous SAT (USAT) is in polynomial time, which is widely conjectured to be unlikely. Finally, we discuss the practicability of this approach. Experimental results are provided.

Precision-sensitive Euclidean shortest path in 3-space (extended abstract)

Abstract: Precision-Sensitive Euclidean Shortest Path in 3-Space *

Contour-based partial object recognition using symmetry in image databases

Abstract: This paper discusses the problem of partial object recognition in image databases. We propose the method to reconstruct and estimate partially occluded shapes and regions of objects in images from overlapping and cutting. We present the robust method for recognizing partially occluded objects based on symmetry properties, which is based on the contours of objects. Our method provides simple techniques to reconstruct occluded regions via a region copy using the symmetry axis within an object. Based on the estimated parameters for partially occluded objects, we perform object recognition on the classification tree. Since our method relies on reconstruction of the object based on the symmetry rather than statistical estimates, it has proven to be remarkably robust in recognizing partially occluded objects in the presence of scale changes, rotation, and viewpoint changes.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Planning Algorithms: Introductory Material

Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed to be able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, for example, the number of digits of the integer to be factored.

Davenport-Schinzel sequences and their geometric applications

Abstract: An $(n,s)$ Davenport--Schinzel sequence, for positive integers $n$ and $s$, is a sequence composed of $n$ symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly non-contiguous) subsequence, any alternation $a \cdots b \cdots a \cdots b \cdots$ of length $s+2$ between two distinct symbols $a$ and $b$. The close relationship between Davenport--Schinzel sequences and the combinatorial structure of lower envelopes of collections of functions make the sequences very attractive, because a wide variety of geometric problems can be formulated in terms of lower envelopes. A close to linear bound on the maximum length of Davenport--Schinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems. This paper gives a comprehensive survey on the theory of Davenport--Schinzel sequences and their geometric applications.