David Eppstein
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Knowledge Spaces Applications in Education Knowledge Spaces
Jean-Claude Falmagne · Dietrich Albert Christopher Doble · David Eppstein Xiangen Hu Editors Knowledge Spaces Applications in Education Knowledge Spaces Jean-Claude Falmagne • Dietrich Albert Christopher Doble • David Eppstein • Xiangen Hu Editors Knowledge Spaces Applications in Education Editors Jean-Claude Falmagne Dietrich Albert School of Social Sciences, Department of Psychology Dept. Cognitive Sciences University of Graz University of California, Irvine Graz, Austria Irvine, CA, USA Christopher Doble David Eppstein ALEKS Corporation Donald Bren School of Information Irvine, CA, USA & Computer Sciences University of California, Irvine Irvine, CA, USA Xiangen Hu Department of Psychology University of Memphis Memphis, TN, USA ISBN 978-3-642-35328-4 ISBN 978-3-642-35329-1 (eBook) DOI 10.1007/978-3-642-35329-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013942001 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. -
Tarjan Transcript Final with Timestamps
A.M. Turing Award Oral History Interview with Robert (Bob) Endre Tarjan by Roy Levin San Mateo, California July 12, 2017 Levin: My name is Roy Levin. Today is July 12th, 2017, and I’m in San Mateo, California at the home of Robert Tarjan, where I’ll be interviewing him for the ACM Turing Award Winners project. Good afternoon, Bob, and thanks for spending the time to talk to me today. Tarjan: You’re welcome. Levin: I’d like to start by talking about your early technical interests and where they came from. When do you first recall being interested in what we might call technical things? Tarjan: Well, the first thing I would say in that direction is my mom took me to the public library in Pomona, where I grew up, which opened up a huge world to me. I started reading science fiction books and stories. Originally, I wanted to be the first person on Mars, that was what I was thinking, and I got interested in astronomy, started reading a lot of science stuff. I got to junior high school and I had an amazing math teacher. His name was Mr. Wall. I had him two years, in the eighth and ninth grade. He was teaching the New Math to us before there was such a thing as “New Math.” He taught us Peano’s axioms and things like that. It was a wonderful thing for a kid like me who was really excited about science and mathematics and so on. The other thing that happened was I discovered Scientific American in the public library and started reading Martin Gardner’s columns on mathematical games and was completely fascinated. -
Drawing Graphs and Maps with Curves
Report from Dagstuhl Seminar 13151 Drawing Graphs and Maps with Curves Edited by Stephen Kobourov1, Martin Nöllenburg2, and Monique Teillaud3 1 University of Arizona – Tucson, US, [email protected] 2 KIT – Karlsruhe Institute of Technology, DE, [email protected] 3 INRIA Sophia Antipolis – Méditerranée, FR, [email protected] Abstract This report documents the program and the outcomes of Dagstuhl Seminar 13151 “Drawing Graphs and Maps with Curves”. The seminar brought together 34 researchers from different areas such as graph drawing, information visualization, computational geometry, and cartography. During the seminar we started with seven overview talks on the use of curves in the different communities represented in the seminar. Abstracts of these talks are collected in this report. Six working groups formed around open research problems related to the seminar topic and we report about their findings. Finally, the seminar was accompanied by the art exhibition Bending Reality: Where Arc and Science Meet with 40 exhibits contributed by the seminar participants. Seminar 07.–12. April, 2013 – www.dagstuhl.de/13151 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling, G.2.2 Graph Theory, F.2.2 Nonnumerical Algorithms and Problems Keywords and phrases graph drawing, information visualization, computational cartography, computational geometry Digital Object Identifier 10.4230/DagRep.3.4.34 Edited in cooperation with Benjamin Niedermann 1 Executive Summary Stephen Kobourov Martin Nöllenburg Monique Teillaud License Creative Commons BY 3.0 Unported license © Stephen Kobourov, Martin Nöllenburg, and Monique Teillaud Graphs and networks, maps and schematic map representations are frequently used in many fields of science, humanities and the arts. -
On the Density of a Graph and Its Blowup
On the Density of a Graph and its Blowup Asaf Shapira ¤ Raphael Yustery Abstract It is well-known that, of all graphs with edge-density p, the random graph G(n; p) contains the smallest density of copies of Kt;t, the complete bipartite graph of size 2t. Since Kt;t is a t-blowup of an edge, the following intriguing open question arises: Is it true that of all graphs with triangle 3 density p , the random graph G(n; p) contains close to the smallest density of Kt;t;t, which is the t-blowup of a triangle? Our main result gives an indication that the answer to the above question is positive by showing that for some blowup, the answer must be positive. More formally we prove that if G 3 has triangle density p , then there is some 2 · t · T (p) for which the density of Kt;t;t in G is at (3+o(1))t2 least p , which (up to the o(1) term) equals the density of Kt;t;t in G(n; p). We also raise several open problems related to these problems and discuss some applications to other areas. 1 Introduction One of the main family of problems studied in extremal graph theory is how does the lack and/or number of copies of one graph H in a graph G a®ect the lack and/or number of copies of another graph H0 in G. Perhaps the most well known problems of this type are Ramsey's Theorem and Tur¶an'sTheorem. -
Closest 4-Leaf Power Is Fixed-Parameter Tractable$
Discrete Applied Mathematics 156 (2008) 3345–3361 www.elsevier.com/locate/dam Closest 4-leaf power is fixed-parameter tractableI Michael Dom∗, Jiong Guo, Falk Huffner,¨ Rolf Niedermeier Institut fur¨ Informatik, Friedrich-Schiller-Universitat¨ Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany Received 3 August 2006; received in revised form 18 December 2007; accepted 9 January 2008 Available online 4 March 2008 Abstract The NP-complete CLOSEST 4-LEAF POWER problem asks, given an undirected graph, whether it can be modified by at most r edge insertions or deletions such that it becomes a 4-leaf power. Herein, a 4-leaf power is a graph that can be constructed by considering an unrooted tree—the 4-leaf root—with leaves one-to-one labeled by the graph vertices, where we connect two graph vertices by an edge iff their corresponding leaves are at distance at most 4 in the tree. Complementing previous work on CLOSEST 2-LEAF POWER and CLOSEST 3-LEAF POWER, we give the first algorithmic result for CLOSEST 4-LEAF POWER, showing that CLOSEST 4-LEAF POWER is fixed-parameter tractable with respect to the parameter r. c 2008 Elsevier B.V. All rights reserved. Keywords: Fixed-parameter tractability; Graph algorithm; Graph modification; Graph power; Leaf power; Forbidden subgraph characterization 1. Introduction Graph powers form a classical concept in graph theory, and the rich literature dates back to the sixties of the previous century (see [5, Section 10.6] and [27] for surveys). The k-power of an undirected graph G D .V; E/ is the undirected graph Gk D .V; E0/ with .u; v/ 2 E0 iff there is a path of length at most k between u and v in G. -
The Best Nurturers in Computer Science Research
The Best Nurturers in Computer Science Research Bharath Kumar M. Y. N. Srikant IISc-CSA-TR-2004-10 http://archive.csa.iisc.ernet.in/TR/2004/10/ Computer Science and Automation Indian Institute of Science, India October 2004 The Best Nurturers in Computer Science Research Bharath Kumar M.∗ Y. N. Srikant† Abstract The paper presents a heuristic for mining nurturers in temporally organized collaboration networks: people who facilitate the growth and success of the young ones. Specifically, this heuristic is applied to the computer science bibliographic data to find the best nurturers in computer science research. The measure of success is parameterized, and the paper demonstrates experiments and results with publication count and citations as success metrics. Rather than just the nurturer’s success, the heuristic captures the influence he has had in the indepen- dent success of the relatively young in the network. These results can hence be a useful resource to graduate students and post-doctoral can- didates. The heuristic is extended to accurately yield ranked nurturers inside a particular time period. Interestingly, there is a recognizable deviation between the rankings of the most successful researchers and the best nurturers, which although is obvious from a social perspective has not been statistically demonstrated. Keywords: Social Network Analysis, Bibliometrics, Temporal Data Mining. 1 Introduction Consider a student Arjun, who has finished his under-graduate degree in Computer Science, and is seeking a PhD degree followed by a successful career in Computer Science research. How does he choose his research advisor? He has the following options with him: 1. Look up the rankings of various universities [1], and apply to any “rea- sonably good” professor in any of the top universities. -
Lecture Notes in Computer Science
D. Dolev Z. Galil M. Rodeh (Eds.) Theory of Computing and Systems ISTCS '92, Israel Symposium Haifa, Israel, May 27-28, 1992 Proceedings Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest Series Editors Gerhard Goos Juris Hartmanis Universit~it Karlsruhe Department of Computer Science Postfach 69 80 Cornell University Vincenz-Priessnitz-Stral3e 1 5149 Upson Hall W-7500 Karlsruhe, FRG Ithaca, NY 14853, USA Volume Editors Danny Dolev Hebrew University Givat Ram, Jerusalem, Israel Zvi Galil Columbia University, New York, NY 10027, USA and Tel Aviv University Ramat Aviv, Tel Aviv, Israel Michael Rodeh IBM Israel Ltd., Science and Technology, Technion City Haifa 32000, Israel CR Subject Classification (1991): F.1-4, B.3, C.2, G.1-2, 1.1, E.4, D.2-3 ISBN 3-540-55553-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-55553-6 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1992 Printed in Germany Typesetting: Camera ready by author/editor Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. -
Forbidden Configurations in Discrete Geometry
FORBIDDEN CONFIGURATIONS IN DISCRETE GEOMETRY This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry and listing many open prob- lems. It unifies these mathematical and computational views using for- bidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of fig- ures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathe- matics including number theory, graph theory, and the theory of per- mutation patterns. Pseudocode is included for many algorithms that compute properties of point sets. David Eppstein is Chancellor’s Professor of Computer Science at the University of California, Irvine. He has more than 350 publications on subjects including discrete and computational geometry, graph the- ory, graph algorithms, data structures, robust statistics, social network analysis and visualization, mesh generation, biosequence comparison, exponential algorithms, and recreational mathematics. He has been the moderator for data structures and algorithms -
Graphs in Nature
Graphs in Nature David Eppstein University of California, Irvine Symposium on Geometry Processing, July 2019 Inspiration: Steinitz's theorem Purely combinatorial characterization of geometric objects: Graphs of convex polyhedra are exactly the 3-vertex-connected planar graphs Image: Kluka [2006] Overview Cracked surfaces, bubble foams, and crumpled paper also form natural graph-like structures What properties do these graphs have? How can we recognize and synthesize them? I. Cracks and Needles Motorcycle graphs: Canonical quad mesh partitioning Paper at SGP'08 [Eppstein et al. 2008] Problem: partition irregular quad-mesh into regular submeshes Inspiration: Light cycle game from TRON movies Mesh partitioning method Grow cut paths outwards from each irregular (non-degree-4) vertex Cut paths continue straight across regular (degree-4) vertices They stop when they run into another path Result: approximation to optimal partition (exact optimum is NP-complete) Mesh-free motorcycle graphs Earlier... Motorcycles move from initial points with given velocities When they hit trails of other motorcycles, they crash [Eppstein and Erickson 1999] Application of mesh-free motorcycle graphs Initially: A simplified model of the inward movement of reflex vertices in straight skeletons, a rectilinear variant of medial axes with applications including building roof construction, folding and cutting problems, surface interpolation, geographic analysis, and mesh construction Later: Subroutine for constructing straight skeletons of simple polygons [Cheng and Vigneron 2007; Huber and Held 2012] Image: Huber [2012] Construction of mesh-free motorcycle graphs Main ideas: Define asymmetric distance: Time when one motorcycle would crash into another's trail Repeatedly find closest pair and eliminate crashed motorcycle Image: Dancede [2011] O(n17=11+) [Eppstein and Erickson 1999] Improved to O(n4=3+) [Vigneron and Yan 2014] Additional log speedup using mutual nearest neighbors instead of closest pairs [Mamano et al. -
Graph Powers: Hardness Results, Good Characterizations and Efficient Algorithms
Graph Powers: Hardness Results, Good Characterizations and Efficient Algorithms Dissertation zur Erlangung des akademischen Grades Doktor-Ingenieur (Dr.-Ing.) der Fakult¨at f¨ur Informatik und Elektrotechnik der Universit¨at Rostock Vorgelegt von MSc. Ngoc Tuy Nguyen Rostock, November 2009 Gutachter: Prof. Dr. Van Bang Le Universit¨at Rostock. Institut fu¨rInformatik Gutachter: Prof. Dr. Egon Wanke Heinrich- Heine- Universit¨at D¨usseldorf. Institut fu¨rInformatik Gutachter: Prof. Dr. Ekkehard K¨ohler Brandenburgische Technische Universit¨at Cottbus. Institut fu¨rMathematik Tag der ¨offentlichen Verteidigung: 30. Oktober 2009 ii Abstract Given a graph H =(VH , EH ) and a positive integer k, the k-th power of H, written Hk, is the graph obtained from H by adding new edges between any pair of vertices k at distance at most k in H; formally, H =(VH , {xy | 1 ≤ dH (x, y) ≤ k}). A graph G is the k-th power of a graph H if G = Hk, and in this case, H is a k-th root of G. For the cases of k = 2 and k = 3, we say that H2 and H3 is the square, respectively, the cube of H and H is a square root of G = H2, respectively, a cube root of G = H3. In this thesis we study the computational complexity for recognizing k-th pow- ers of general graphs as well as restricted graphs. This work provides new NP- completeness results, good characterizations and efficient algorithms for graph pow- ers. The main results are the following. • There exist reductions proving the NP-completeness for recognizing k-th pow- ers of general graphs for fixed k ≥ 2, recognizing k-th powers of bipartite graphs for fixed k ≥ 3, recognizing k-th powers of chordal graphs, and finding k-th roots of chordal graphs for all fixed k ≥ 2. -
Recognition of C4-Free and 1/2-Hyperbolic Graphs David Coudert, Guillaume Ducoffe
Recognition of C4-free and 1/2-hyperbolic graphs David Coudert, Guillaume Ducoffe To cite this version: David Coudert, Guillaume Ducoffe. Recognition of C4-free and 1/2-hyperbolic graphs. SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2014, 28 (3), pp.1601-1617. 10.1137/140954787. hal-01070768 HAL Id: hal-01070768 https://hal.inria.fr/hal-01070768 Submitted on 2 Oct 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ∗ Recognition of C4-free and 1/2-hyperbolic graphs David Coudert†‡ Guillaume Ducoffe†‡§ October 2, 2014 Abstract The shortest-path metric d of a connected graph G is 1/2-hyperbolic if, and only if, it satisfies d(u,v) + d(x,y) ≤ max{d(u,x) + d(v,y), d(u,y) + d(v,x)} + 1, for every 4-tuple u,x,v,y of G. We show that the problem of deciding whether an unweighted graph is 1/2-hyperbolic is subcubic equivalent to the problem of determining whether there is a chordless cycle of length 4 in a graph. An improved algorithm is also given for both problems, taking advantage of fast rectangular matrix multiplication. -
Sparsification–A Technique for Speeding up Dynamic Graph Algorithms
Sparsification–A Technique for Speeding Up Dynamic Graph Algorithms DAVID EPPSTEIN University of California, Irvine, Irvine, California ZVI GALIL Columbia University, New York, New York GIUSEPPE F. ITALIANO Universita` “Ca’ Foscari” di Venezia, Venice, Italy AND AMNON NISSENZWEIG Tel-Aviv University, Tel-Aviv, Israel Abstract. We provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2-edge connectivity, and bipartiteness in time O(n1/2) per change; 3-edge connectivity, in time O(n2/3) per change; 4-edge connectivity, in time O(na(n)) per change; k-edge connectivity for constant k, in time O(nlogn) per change; 2-vertex connectivity, and 3-vertex connectivity, in time O(n) per change; and 4-vertex connectivity, in time O(na(n)) per change. A preliminary version of this paper was presented at the 33rd Annual IEEE Symposium on Foundations of Computer Science (Pittsburgh, Pa.), 1992. D. Eppstein was supported in part by National Science Foundation (NSF) Grant CCR 92-58355. Z. Galil was supported in part by NSF Grants CCR 90-14605 and CDA 90-24735. G. F. Italiano was supported in part by the CEE Project No. 20244 (ALCOM-IT) and by a research grant from Universita` “Ca’ Foscari” di Venezia; most of his work was done while at IBM T. J. Watson Research Center. Authors’ present addresses: D. Eppstein, Department of Information and Computer Science, University of California, Irvine, CA 92717, e-mail: [email protected], internet: http://www.ics.