Synergistic Solutions on MultiSets

Karp et al. (1988) described Deferred Data Structures for Multisets as "lazy" data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size n and number of queries q fixed. Barbay et al. (2016) refined this approach to take advantage of the gaps between the positions hit by the queries (i.e., the structure in the queries). We develop new techniques in order to further refine this approach and take advantage all at once of the structure (i.e., the multiplicities of the elements), some notions of local order (i.e., the number and sizes of runs) and global order (i.e., the number and positions of existing pivots) in the input; and of the structure and order in the sequence of queries. Our main result is a synergistic deferred data structure which outperforms all solutions in the comparison model that take advantage of only a subset of these features. As intermediate results, we describe two new synergistic sorting algorithms, which take advantage of some notions of structure and order (local and global) in the input, improving upon previous results which take advantage only of the structure (Munro and Spira 1979) or of the local order (Takaoka 1997) in the input; and one new multiselection algorithm which takes advantage of not only the order and structure in the input, but also of the structure in the queries

28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland

Peer reviewe

Efficient Data Structures for Partial Orders, Range Modes, and Graph Cuts

This thesis considers the study of data structures from the perspective of the theoretician, with a focus on simplicity and practicality. We consider both the time complexity as well as space usage of proposed solutions. Topics discussed fall in three main categories: partial order representation, range modes, and graph cuts. We consider two problems in partial order representation. The first is a data structure to represent a lattice. A lattice is a partial order where the set of elements larger than any two elements x and y are all larger than an element z, known as the join of x and y; a similar condition holds for elements smaller than any two elements. Our data structure is the first correct solution that can simultaneously compute joins and the inverse meet operation in sublinear time while also using subquadratic space. The second is a data structure to support queries on a dynamic set of one-dimensional ordered data; that is, essentially any operation computable on a binary search tree. We develop a data structure that is able to interpolate between binary search trees and efficient priority queues, offering more-efficient insertion times than the former when query distribution is non-uniform. We also consider static and dynamic exact and approximate range mode. Given one-dimensional data, the range mode problem is to compute the mode of a subinterval of the data. In the dynamic range mode problem, insertions and deletions are permitted. For the approximate problem, the element returned is to have frequency no less than a factor (1+epsilon) of the true mode, for some epsilon > 0. Our results include a linear-space dynamic exact range mode data structure that simultaneously improves on best previous operation complexity and an exact dynamic range mode data structure that breaks the Theta(n^(2/3)) time per operation barrier. For approximate range mode, we develop a static succinct data structure offering a logarithmic-factor space improvement and give the first dynamic approximate range mode data structure. We also consider approximate range selection. The final category discussed is graph and dynamic graph algorithms. We develop an optimal offline data structure for dynamic 2- and 3- edge and vertex connectivity. Here, the data structure is given the entire sequence of operations in advance, and the dynamic operations are edge insertion and removal. Finally, we give a simplification of Karger's near-linear time minimum cut algorithm, utilizing heavy-light decomposition and iteration in place of dynamic programming in the subroutine to find a minimum cut of a graph G that cuts at most two edges of a spanning tree T of G

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems