Alfredo Viola

LATIN 2000: Theoretical Informatics

Random Structures and Algorithms.- Algorithmic Aspects of Regularity.- Small Maximal Matchings in Random Graphs.- Some Remarks on Sparsely Connected Isomorphism-Free Labeled Graphs.- Analysis of Edge Deletion Processes on Faulty Random Regular Graphs.- Equivalent Conditions for Regularity (Extended Abstract).- Algorithms I.- Cube Packing.- Approximation Algorithms for Flexible Job Shop Problems.- Emerging Behavior as Binary Search Trees Are Symmetrically Updated.- The LCA Problem Revisited.- Combinatorial Designs.- Optimal and Pessimal Orderings of Steiner Triple Systems in Disk Arrays.- Rank Inequalities for Packing Designs and Sparse Triple Systems.- The Anti-Oberwolfach Solution: Pancyclic 2-Factorizations of Complete Graphs.- Web Graph, Graph Theory I.- Graph Structure of the Web: A Survey.- Polynomial Time Recognition of Clique-Width ? 3 Graphs.- On Dart-Free Perfectly Contractile Graphs Extended Abstract.- Graph Theory II.- Edge Colouring Reduced Indifference Graphs.- Two Conjectures on the Chromatic Polynomial.- Finding Skew Partitions Efficiently.- Competitive Analysis, Complexity.- On the Competitive Theory and Practice of Portfolio Selection (Extended Abstract).- Almost k-Wise Independence and Hard Boolean Functions.- Improved Upper Bounds on the Simultaneous Messages Complexity of the Generalized Addressing Function.- Algorithms II.- Multi-parameter Minimum Spanning Trees.- Linear Time Recognition of Optimal L-Restricted Prefix Codes.- Uniform Multi-hop All-to-All Optical Routings in Rings.- A Fully Dynamic Algorithm for Distributed Shortest Paths.- Computational Number Theory, Cryptography.- Integer Factorization and Discrete Logarithms.- Communication Complexity and Fourier Coefficients of the Diffie-Hellman Key.- Quintic Reciprocity and Primality Test for Numbers of the Form .- Determining the Optimal Contrast for Secret Sharing Schemes in Visual Cryptography.- Analysis of Algorithms I.- Average-Case Analysis of Rectangle Packings.- Heights in Generalized Tries and PATRICIA Tries.- On the Complexity of Routing Permutations on Trees by Arc-Disjoint Paths Extended Abstract.- Algebraic Algorithms.- Subresultants Revisited.- A Unifying Framework for the Analysis of a Class of Euclidean Algorithms.- Worst-Case Complexity of the Optimal LLL Algorithm.- Computability.- Iteration Algebras Are Not Finitely Axiomatizable.- Undecidable Problems in Unreliable Computations.- Automata, Formal Languages.- Equations in Free Semigroups with Anti-involution and Their Relation to Equations in Free Groups.- Squaring Transducers: An Efficient Procedure for Deciding Functionality and Sequentiality of Transducers.- Unambiguous Buchi Automata.- Linear Time Language Recognition on Cellular Automata with Restricted Communication.- Logic, Programming Theory.- From Semantics to Spatial Distribution.- On the Expressivity and Complexity of Quantitative Branching-Time Temporal Logics.- A Theory of Operational Equivalence for Interaction Nets.- Analysis of Algorithms II.- Run Statistics for Geometrically Distributed Random Variables.- Generalized Covariances of Multi-dimensional Brownian Excursion Local Times.- Combinatorics of Geometrically Distributed Random Variables: Length of Ascending Runs.

The diagonal Poisson transform and its application to the analysis of a hashing scheme

We present an analysis of the effect of the last-come-first-served heuristic on a linear probing hash table. We study the behavior of successful searches, assuming searches for all elements of the table are equally likely. It is known that the Robin Hood heuristic achieves minimum variance over all linear probing algorithms. We show that the last-come-first-served heuristic achieves this minimum up to lower-order terms. An accurate analysis of this algorithm is made by introducing a new transform which we call the Diagonal Poisson Transform as it resembles the Poisson Transform. We present important properties of this transform, as well as its application to solve some classes of recurrences, find inverse relations, find asymptotics, and obtain several generalizations of Abels summation formula. We feel the introduction of this transform is the main contribution of the paper.

Adaptive sampling strategies for quickselects

Quickselect with median-of-3 is largely used in practice and its behavior is fairly well understood. However, the following natural adaptive variant, which we call proportion-from-3, had not been previously analyzed: “choose as pivot the smallest of the sample if the relative rank of the sought element is below 1/3, the largest if the relative rank is above 2/3, and the median if the relative rank is between 1/3 and 2/3.” We first analyze the average number of comparisons made when using proportion-from-2 and then for proportion-from-3. We also analyze ν-find, a generalization of proportion-from-3 with interval breakpoints at ν and 1-ν. We show that there exists an optimal value of ν and we also provide the range of values of ν where ν-find outperforms median-of-3. Then, we consider the average total cost of these strategies, which takes into account the cost of both comparisons and exchanges. Our results strongly suggest that a suitable implementation of ν-find could be the method of choice in a practical setting. We also study the behavior of proportion-from-s with s>3 and in particular we show that proportion-from-s-like strategies are optimal when s→∞.

Analysis of Rabin's Polynomial Irreducability Test

We give a precise average-case analysis of Rabins algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We provide upper and lower bounds for this probability. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case behavior of Rabins variants presented by von zur Gathen & Shoup and by Gao & Panario.

The analysis of linear probing hashing with buckets

Abstract. We present the first exact analysis of a linear probing hashing scheme with buckets of size b . From the generating function for the Robin Hood heuristic we obtain exact expressions for the cost of successful searches. For a full table, with the help of Singularity Analysis, we find the asymptotic expansion of this cost up to O((bm)-1) . We conclude with a new approach to study certain recurrences that involve truncated exponentials. A new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers is introduced. These numbers may prove helpful in studying recurrences involving truncated generating functions.

Preface-S.I.: LATIN 2014

This special issue contains the journal versions of a selection of papers from the 11th Latin American Symposium on Theoretical Informatics (LATIN), held on March 31–April 4 2014, in Montevideo, Uruguay. The conference covered a broad range of topics in theoretical computer science, including algorithms, analytic and enumerative combinatorics, analysis of algorithms, approximation algorithms, automata theory, combinatorics and graph theory, complexity theory, computability, computational algebra, computational geometry, data structures, graph drawing, and random structures. Eight papers were selected for this special issue, all of which went through the thorough reviewing process that is the standard for Algorithmica. The selection was based on two criteria: the quality of the manuscripts and the desire to give readers a sense of the breadth and depth of the topics covered by LATIN. The overview that follows underscores these points In A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters, Cheilaris, Khramtcova, Langerman and Papadopoulou present a construction based on point location, that computes this diagram in expected O(n log2 n) time and expected O(n) space. Their techniques efficiently handle nonstandard characteristics of generalizedVoronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions. The conjugacy problem asks whether two words over generators of a fixed group G are conjugated. In Conjugacy in Baumslag’s group, generic case complexity,

The effect of deletions on different insertion disciplines for hash tables (Extended Abstract)

Abstract Abstract Deletions in open addressing hash tables are often handled by marking the cells as “deleted” instead of “empty”, because otherwise the search algorithm might fail to find some of the keys. The space used by deleted cells may be reused by subsequent insertions. Intuitively, search times should deteriorate as tables become contaminated with deleted cells and, as Knuth points out, in the long run the average successful search time should approach the average unsuccessful search time. We analize the effect of a long sequence of deletions and insertions over tables that use one of three insertion disciplines: standard “first-come-first-served” (FCFS)[2], “last-come-first-served” (LCFS)[3] and “Robin Hood” (RH)[1]. We show that deletions have the predicted effect over the average search cost, but their effect over the variance differs according to the insertion discipline used. When no deletions are allowed, FCFS has a very dispersed distribution, while those of LCFS and RH are very concentrated. But we show that, after many deletions and insertions, both FCFS and LCFS approach a common steady state with high dispersion, while the distribution of RH remains concentrated. We also study the transient behaviors of these methods, doing both an asymptotic and an exact analysis.