On Some Fine-Grained Questions in Algorithms and Complexity
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Curriculum Vitae 01/13/2014
Curriculum Vitae 01/13/2014 Dimitris Papamichail Assistant Professor Department of Computer Science The College of New Jersey P.O. Box 7718 Ewing, NJ 08628-0718, USA Phone (office): (609) 771-2268 E-mail: [email protected] Webpage: www.tcnj.edu/~papamicd RESEARCH INTERESTS Applied algorithms, data structures, computational biology. EDUCATION Ph.D. Computer Science, SUNY at Stony Brook, USA, 8/02-8/07 M.S. Computer Science, University of Arizona, USA, 8/96-5/98 B.E. Computer Engineering and Informatics, University of Patras, Greece, 9/91-6/96 WORK EXPERIENCE • Assistant Professor, Department of Computer Science, The College of New Jersey, 8/13 – present. • Assistant Professor, Department of Computer Science, University of Miami, 8/07 – 8/13 • Research Assistant, Brookhaven National Laboratory, Upton, USA, 10/04 - 8/07 • Research Assistant, Computer Science department, SUNY at Stony Brook, Stony Brook, USA, 9/03 - 8/07 • Teaching Assistant, Computer Science department, SUNY at Stony Brook, Stony Brook, USA, 8/02 - 7/03 • Computer Programmer, Division of Research and Informatics, Greek Army, Greece, 9/00 - 3/02 • Site Engineer, Modular Mining Systems Inc., Tucson, Arizona, USA, 8/98 - 4/00 • Teaching assistant, Computer Science department, University of Arizona, Arizona, USA, 8/97 - 5/98 • Programmer, Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona, USA, 1/97 - 6/97 • Programmer, National Electric Company of Greece, Athens, Greece, 6/94 - 8/94 • Systems Operator, Computer Institute of Technology, Patras, Greece, 6/92 - 9/93 AWARDS/DISTINCTIONS • University of Miami Faculty Learning Community (FLC) Fellow, 2010. • Best paper award, Graduate Research Conference 2004, Computer Science Department, Stony Brook University. -
Algorithms & Computational Complexity
Computational Complexity O ΩΘ Russell Buehler January 5, 2015 2 Chapter 1 Preface What follows are my personal notes created during my undergraduate algorithms course and later an independent study under Professor Holliday as a graduate student. I am not a complexity theorist; I am a graduate student with some knowledge who is–alas–quite fallible. Accordingly, this text is made available as a convenient reference, set of notes, and summary, but without even the slightest hint of a guarantee that everything contained within is factual and correct. This said, if you find an error, I would much appreciate it if you let me know so that it can be corrected. 3 4 CHAPTER 1. PREFACE Contents 1 Preface 3 2 A Brief Review of Algorithms 1 2.1 Algorithm Analysis............................................1 2.1.1 O-notation............................................1 2.2 Common Structures............................................3 2.2.1 Graphs..............................................3 2.2.2 Trees...............................................4 2.2.3 Networks.............................................4 2.3 Algorithms................................................6 2.3.1 Greedy Algorithms........................................6 2.3.2 Dynamic Programming...................................... 10 2.3.3 Divide and Conquer....................................... 12 2.3.4 Network Flow.......................................... 15 2.4 Data Structures.............................................. 17 3 Deterministic Computation 19 3.1 O-Notation............................................... -
Complexity Theory in Computer Science Pdf
Complexity theory in computer science pdf Continue Complexity is often used to describe an algorithm. One could hear something like my sorting algorithm working in n2n'2n2 time in complexity, it's written as O (n2)O (n'2)O (n2) and polynomial work time. Complexity is used to describe the use of resources in algorithms. In general, the resources of concern are time and space. The complexity of the algorithm's time is the number of steps it must take to complete. The cosmic complexity of the algorithm represents the amount of memory the algorithm needs to work. The complexity of the algorithm's time describes how many steps the algorithm should take with regard to input. If, for example, each of the nnn elements entered only works once, this algorithm will take time O'n)O(n)O(n). If, for example, the algorithm has to work on one input element (regardless of input size), it is a constant time, or O(1)O(1)O(1), the algorithm, because regardless of the size of the input, only one is done. If the algorithm performs nnn-operations for each of the nnn elements injected into the algorithm, then this algorithm is performed in time O'n2)O (n2). In the design and analysis of algorithms, there are three types of complexities that computer scientists think: the best case, the worst case, and the complexity of the average case. The best, worst and medium complexity complexity can describe the time and space this wiki will talk about in terms of the complexity of time, but the same concepts can be applied to the complexity of space. -
LSPACE VS NP IS AS HARD AS P VS NP 1. Introduction in Complexity
LSPACE VS NP IS AS HARD AS P VS NP FRANK VEGA Abstract. The P versus NP problem is a major unsolved problem in com- puter science. This consists in knowing the answer of the following question: Is P equal to NP? Another major complexity classes are LSPACE, PSPACE, ESPACE, E and EXP. Whether LSPACE = P is a fundamental question that it is as important as it is unresolved. We show if P = NP, then LSPACE = NP. Consequently, if LSPACE is not equal to NP, then P is not equal to NP. According to Lance Fortnow, it seems that LSPACE versus NP is easier to be proven. However, with this proof we show this problem is as hard as P versus NP. Moreover, we prove the complexity class P is not equal to PSPACE as a direct consequence of this result. Furthermore, we demonstrate if PSPACE is not equal to EXP, then P is not equal to NP. In addition, if E = ESPACE, then P is not equal to NP. 1. Introduction In complexity theory, a function problem is a computational problem where a single output is expected for every input, but the output is more complex than that of a decision problem [6]. A functional problem F is defined as a binary relation (x; y) 2 R over strings of an arbitrary alphabet Σ: R ⊂ Σ∗ × Σ∗: A Turing machine M solves F if for every input x such that there exists a y satisfying (x; y) 2 R, M produces one such y, that is M(x) = y [6]. -
Curriculum Vitae
1 CURRICULUM VITAE Name: StevenSkiena Date of birth: January 30, 1961 Office: Dept. of Computer Science Home: 6Storyland Lane StonyBrook University Setauket, NY 11733 StonyBrook, NY 11794 Tel.: (631) 689-5477 Tel.: (631)-632-8470/9026 email: [email protected] URL: http://www.cs.stonybrook.edu/˜skiena Education University of Illinois at Urbana-Champaign, Fall 1983 to Spring 1988. M.S. in Computer Science May 1985, Ph.D in Computer Science May 1988. Cumulative GPA 4.87/5.00. University of Virginia, Charlottesville VA, Fall 1979 to Spring 1983. B.S. in Computer Science with High Distinction, May 1983. Final GPA3.64/4.0, with 4.0+ GPAinComputer Science. Rodman Scholar,Intermediate Honors, Tau Beta Pi. Employment Founding Director,Institute for AI-DrivenDiscovery and Innovation (IAIDDI), August 2018 to date. College of Engineering and Applied Science, StonyBrook University. StonyBrook University,Empire Innovation Professor,fall 2018 to date. Distinguished Teaching Pro- fessor of Computer Science, spring 2009 to date. Professor of Computer Science, fall 2001 to spring 2009. Associate Professor of Computer Science, fall 1994 to spring 2001. Assistant Professor of Computer Science, fall 1988 to spring 1994. Also, Adjunct Professor of Applied Mathematics, spring 1991 to date. Affiliated faculty,Dept. of Biomedical Engineering, Institute for Advanced Computa- tional Science (IACS), and Graduate Program in Genetics. Yahoo Labs/Research, Visiting Scientist, NewYork, NY.summer 2015 to summer 2016. Chief Scientist, General Sentiment Inc. (www.generalsentiment.com) Woodbury NY spring 2009 to spring 2015. Hong Kong University of Science and Technology (HKUST), Visiting Professor,Dept. of Computer Science and Engineering, fall 2008 to summer 2009. -
Counting Below #P: Classes, Problems and Descriptive Complexity
Msc Thesis Counting below #P : Classes, problems and descriptive complexity Angeliki Chalki µΠλ8 Graduate Program in Logic, Algorithms and Computation National and Kapodistrian University of Athens Supervised by Aris Pagourtzis Advisory Committee Dimitris Fotakis Aris Pagourtzis Stathis Zachos September 2016 Abstract In this thesis, we study counting classes that lie below #P . One approach, the most regular in Computational Complexity Theory, is the machine-based approach. Classes like #L, span-L [1], and T otP ,#PE [38] are defined establishing space and time restrictions on Turing machine's computational resources. A second approach is Descriptive Complexity's approach. It characterizes complexity classes by the type of logic needed to express the languages in them. Classes deriving from this viewpoint, like #FO [44], #RHΠ1 [16], #RΣ2 [44], are equivalent to #P , the class of AP - interriducible problems to #BIS, and some subclass of the problems owning an FPRAS respectively. A great objective of such an investigation is to gain an understanding of how “efficient counting" relates to these already defined classes. By “efficient counting" we mean counting solutions of a problem using a polynomial time algorithm or an FPRAS. Many other interesting properties of the classes considered and their problems have been examined. For example alternative definitions of counting classes using relation-based op- erators, and the computational difficulty of complete problems, since complete problems capture the difficulty of the corresponding class. Moreover, in Section 3.5 we define the log- space analog of the class T otP and explore how and to what extent results can be transferred from polynomial time to logarithmic space computation. -
The Complexity of Counting Poset and Permutation Patterns
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 64(1) (2016), Pages 154–165 The complexity of counting poset and permutation patterns Joshua Cooper Anna Kirkpatrick Mathematics Department University of South Carolina 1523 Greene St., Columbia, SC 29208 U.S.A. Abstract We introduce a notion of pattern occurrence that generalizes both clas- sical permutation patterns as well as poset containment. Many ques- tions about pattern statistics and avoidance generalize naturally to this setting, and we focus on functional complexity problems – particularly those that arise by constraining the order dimensions of the pattern and text posets. We show that counting the number of induced, injective occurrences among dimension-2 posets is #P-hard; enumerating the lin- ear extensions that occur in realizers of dimension-2 posets can be done in polynomial time, while for unconstrained dimension it is GI-complete; counting not necessarily induced, injective occurrences among dimension- 2posetsis#P-hard; counting injective or not necessarily injective occur- rences of an arbitrary pattern in a dimension-1 text is #P-hard, although it is in FP if the pattern poset is constrained to have bounded intrinsic width; and counting injective occurrences of a dimension-1 pattern in an arbitrary text is #P-hard, while it is in FP for bounded-dimension texts. This framework naturally leads to a number of open questions, chief among which are (1) is it #P-hard to count the number of oc- currences of a dimension-2 pattern in a dimension-1 text, and (2) is it #P-hard to count the number of permutations avoiding a given pattern? 1 Introduction A tremendous amount of study has been dedicated to understanding occurrence or non-occurrence of combinatorial substructures: which substructures are avoidable and counting objects that avoid them, what substructures random and random- like objects possess, enumerating substructures in general objects, describing the subclass of objects that have particular substructure counts, etc. -
The Computational Complexity of Games and Markets: an Introduction for Economists
The Computational Complexity of Games and Markets: An Introduction for Economists Andrew McLennan∗ University of Queensland December 2011 Abstract This is an expository survey of recent results in computer science related to the computation of fixed points, with the central one beingthat the problemof finding an approximate Nash equilibrium of a bimatrix game is PPAD-complete. This means that this problem is, in a certain sense, as hard as any fixed point problem. Subsequently many other problems have been shown to be PPAD- complete, including finding Walrasian equilibria in certain simple exchange economies. We also comment on the scientific consequences of complexity as a barrier to equilibration, and other sorts of complexity, for our understanding of how markets operate. It is argued that trading in complex systems of markets should be analogized to games such as chess, go, bridge, and poker, in which the very best players are much better than all but a small number of competitors. These traders make positive rents, and their presence is a marker of complexity. Consequences for the efficient markets hypothesis are sketched. Running Title: Complexity of Games and Markets Journal of Economic Literature Classification Numbers G12 and G14. Keywords: Computational complexity, two person games, Nash equilibrium, Scarf algorithm, NP, TFNP, PPAD, FPTAS, Lemke-Howson algorithm, Walrasian equilibrium, arbitrage, asset trading, efficient market hypothesis. ∗School of Economics, Level 6 Colin Clark Building, University of Queensland, QLD 4072 Australia, [email protected]. McLennan’s work was funded in part by Australian Research Council grant DP0773324. I would like to gratefully acknowledge the comments received at Games Toulouse 2011, and at seminar pre- sentations at the Australian National University, the Institute for Social and Economic Research at Osaka University, and the Kyoto Institute for Economic Research. -
Curriculum Vitae
Curriculum Vitae Dimitris Papamichail Assistant Professor Department of Computer Science 6000 SW 76th St University of Miami South Miami, FL 33143, USA P.O. Box 248154 Phone (cell): (631) 428-4962 Coral Gables, FL 33124-4245, USA Phone (home): (305) 667-7042 Phone (office): (305) 284-4189 e-mail: [email protected] webpage: www.cs.miami.edu/~dimitris Research Interests Bioinformatics, algorithms and data structures, optimization, decision support systems. Education Ph.D. Computer Science, SUNY at Stony Brook, USA, 8/02-8/07 M.S. Computer Science, University of Arizona, USA, 8/96-5/98 B.E. Computer Engineering and Informatics, University of Patras, Greece, 9/91-6/96 Work Experience Assistant Professor, Department of Computer Science, University of Miami, 08/07-date Research Assistant, Brookhaven National Laboratory, Upton, USA, 10/04-8/07 Research Assistant, Computer Science department, SUNY at Stony Brook, Stony Brook, USA, 9/03-8/07 Teaching Assistant, Computer Science department, SUNY at Stony Brook, Stony Brook, USA, 8/02-7/03 Computer Programmer, Division of Research and Informatics, Greek Army, Greece, 9/00-3/02 Site Engineer, Modular Mining Systems Inc., Tucson, Arizona, USA, 8/98-4/00 Teaching assistant, Computer Science department, University of Arizona, Arizona, USA, 8/97-5/98 Programmer, Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona, USA, 1/97- 6/97 Programmer, National Electric Company of Greece, Athens, Greece, 6/94-8/94 Systems Operator, Computer Institute of Technology, Patras, Greece, 6/92-9/93 Awards/Distinctions Best paper award, Graduate Research Conference 2004, Computer Science Dept. SUNY at Stony Brook. -
Who's Bigger? a Quantitative Analysis of Historical Fame
Who's Bigger? A Quantitative Analysis of Historical Fame Who's Bigger? A Quantitative Analysis of Historical Fame Steven Skiena1 Charles Ward1 1 Department of Computer Science Stony Brook University Stony Brook, NY 11794-4400 September 5, 2012 Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Outline 1 Warmup 2 Methodology 3 Applications Trends Analysis Evaluating Human Selection Processes Gender Imbalance in Wikipedia 4 Conclusions Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Who's Bigger: Historical Rankings Numerical ratings/rankings provide a way to focus greater attention on the best/most important things. Rankings are highly subjective and culturally biased, yet rankings provide a popular mix of education and entertainment. We seek algorithms to construct informative and meaningful historical rankings of all the people described in Wikipedia. George Washington (1732{1799) [6] Abraham Lincoln (1809{1865) [5]* Chester A. Arthur (1829{1886) [490] Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Who's Bigger? (Presidents) Battle: George Washington vs. Abraham Lincoln Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Who's Bigger? (Presidents) Battle: George Washington vs. Abraham Lincoln George Washington (1732{1799) [6] Abraham Lincoln (1809{1865) [5]* Chester A. Arthur (1829{1886) [490] Jesus (7 B.C.{30 A.D.) [1]* John Lennon (1940{1980) [141] Paul McCartney (1942{ ) [399] George Harrison (1943{2001) [615] Ringo Starr (1940{ ) [1729] Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Are the Beatles \Bigger than Jesus"? Battle: Jesus vs. John Lennon Who's Bigger? A Quantitative Analysis of Historical Fame Warmup Are the Beatles \Bigger than Jesus"? Battle: Jesus vs. -
Lipics-ITCS-2021-44.Pdf (0.6
Total Functions in the Polynomial Hierarchy Robert Kleinberg Cornell University, Ithaca, NY, USA Oliver Korten Columbia University, New York, NY, USA Daniel Mitropolsky Columbia University, New York, NY, USA Christos Papadimitriou Columbia University, New York, NY, USA Abstract We identify several genres of search problems beyond NP for which existence of solutions is guaranteed. One class that seems especially rich in such problems is PEPP (for “polynomial empty pigeonhole principle”), which includes problems related to existence theorems proved through the union bound, such as finding a bit string that is far from all codewords, finding an explicit rigid matrix, as well as a problem we call Complexity, capturing Complexity Theory’s quest. When the union bound is generous, in that solutions constitute at least a polynomial fraction of the domain, we have a family of seemingly weaker classes α-PEPP, which are inside FPNP|poly. Higher in the hierarchy, we identify the constructive version of the Sauer-Shelah lemma and the appropriate generalization of PPP that contains it, as well as the problem of finding a king in a tournament (a vertex k such that all other vertices are defeated by k, or by somebody k defeated). 2012 ACM Subject Classification Theory of computation → Complexity classes Keywords and phrases total complexity, polynomial hierarchy, pigeonhole principle Digital Object Identifier 10.4230/LIPIcs.ITCS.2021.44 Funding Daniel Mitropolsky: This research was supported in part by a grant from the Columbia-IBM center for Blockchain and Data Transparency, and by JPMorgan Chase & Co. This research was supported in part by NSF Awards CCF1763970 andCCF1910700, and by a research contract with Softbank Christos Papadimitriou: This research was supported in part by NSF Awards CCF1763970 and- CCF1910700, and by a research contract with Softbank. -
Programming Challenges (PDF)
TEXTS IN COMPUTER SCIENCE Editors David Gries Fred B. Schneider Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo This page intentionally left blank Steven S. Skiena Miguel A. Revilla PROGRAMMING CHALLENGES The Programming Contest Training Manual With 65 Illustrations Steven S. Skiena Miguel A. Revilla Department of Computer Science Department of Applied Mathematics SUNY Stony Brook and Computer Science Stony Brook, NY 11794-4400, USA Faculty of Sciences [email protected] University of Valladolid Valladolid, 47011, SPAIN [email protected] Series Editors: David Gries Fred B. Schneider Department of Computer Science Department of Computer Science 415 Boyd Graduate Studies Upson Hall Research Center Cornell University The University of Georgia Ithaca, NY 14853-7501, USA Athens, GA 30602-7404, USA Cover illustration: “Spectator,” by William Rose © 2002. Library of Congress Cataloging-in-Publication Data Skeina, Steven S. Programming challenges : the programming contest training manual / Steven S. Skiena, Miguel A. Revilla. p. cm. — (Texts in computer science) Includes bibliographical references and index. ISBN 0-387-00163-8 (softcover : alk. paper) 1. Computer programming. I. Revilla, Miguel A. II. Title. III. Series. QA76.6.S598 2003 005.1—dc21 2002044523 ISBN 0-387-00163-8 Printed on acid-free paper. © 2003 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.