Structures In Computer Science Research Articles

Iceberg Hashing: Optimizing Many Hash-Table Criteria at Once

Despite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different trade-offs have been proposed. This article introduces Iceberg hashing, a hash table that simultaneously offers the strongest known guarantees on a large number of core properties. Iceberg hashing supports constant-time operations while improving on the state of the art for space efficiency, cache efficiency, and low failure probability. Iceberg hashing is also the first hash table to support a load factor of up to 1 - o(1) while being stable, meaning that the position where an element is stored only ever changes when resizes occur. In fact, in the setting where keys are Θ (log n ) bits, the space guarantees that Iceberg hashing offers, namely that it uses at most \(\log \binom{|U|}{n} + O(n \log \ \text{log} n)\) bits to store n items from a universe U , matches a lower bound by Demaine et al. that applies to any stable hash table. Iceberg hashing introduces new general-purpose techniques for some of the most basic aspects of hash-table design. Notably, our indirection-free technique for dynamic resizing, which we call waterfall addressing, and our techniques for achieving stability and very-high probability guarantees, can be applied to any hash table that makes use of the front-yard/backyard paradigm for hash table design.

Two-level type theory and applications

AbstractWe define and develop two-level type theory (2LTT), a version of Martin-Löf type theory which combines two different type theories. We refer to them as the ‘inner’ and the ‘outer’ type theory. In our case of interest, the inner theory is homotopy type theory (HoTT) which may include univalent universes and higher inductive types. The outer theory is a traditional form of type theory validating uniqueness of identity proofs (UIP). One point of view on it is as internalised meta-theory of the inner type theory. There are two motivations for 2LTT. Firstly, there are certain results about HoTT which are of meta-theoretic nature, such as the statement that semisimplicial types up to level n can be constructed in HoTT for any externally fixed natural number n. Such results cannot be expressed in HoTT itself, but they can be formalised and proved in 2LTT, where n will be a variable in the outer theory. This point of view is inspired by observations about conservativity of presheaf models. Secondly, 2LTT is a framework which is suitable for formulating additional axioms that one might want to add to HoTT. This idea is heavily inspired by Voevodsky’s Homotopy Type System (HTS), which constitutes one specific instance of a 2LTT. HTS has an axiom ensuring that the type of natural numbers behaves like the external natural numbers, which allows the construction of a universe of semisimplicial types. In 2LTT, this axiom can be assumed by postulating that the inner and outer natural numbers types are isomorphic. After defining 2LTT, we set up a collection of tools with the goal of making 2LTT a convenient language for future developments. As a first such application, we develop the theory of Reedy fibrant diagrams in the style of Shulman. Continuing this line of thought, we suggest a definition of $(\infty,1)$ -category and give some examples.

On knot-free vertex deletion: Fine-grained parameterized complexity analysis of a deadlock resolution graph problem

A knot in a directed graph G is a strongly connected subgraph Q of G with size at least two, such that no vertex in V(Q) is an in-neighbor of a vertex in V(G)∖V(Q). Knots are important graph structures in Computer Science because they characterize the existence of deadlocks in a classical distributed computation model, the so-called OR-model. Given a directed graph G, and a positive integer k, the Knot-Free Vertex Deletion (KFVD) problem consists of determining whether G has a subset S⊆V(G) with size at most k such that G[V∖S] contains no knot. KFVD is an NP-complete graph problem with natural applications in deadlock resolution. In this paper, we present a parameterized complexity analysis of KFVD. We prove that: KFVD is W[1]-hard when parameterized by the size of the solution; it can be solved in 2klog⁡φ⋅nO(1) time, but assuming SETH, it cannot be solved in (2−ϵ)klog⁡φ⋅nO(1) time, where φ is the size of the largest strongly connected subgraph of G; it can be solved in 2ϕ⋅nO(1) time, but assuming ETH, it cannot be solved in 2o(ϕ)⋅nO(1) time, where ϕ is the number of vertices with out-degree at most k; it can be solved in 2O(twlog⁡tw)⋅nO(1) time, but assuming ETH it cannot be solved in 2o(tw)⋅nO(1) time, where tw is the treewidth of the underlying undirected graph; and, it can be solved in FPT time when parameterized by the clique-width of the directed graph. In addition, lower bounds for kernelization are also provided.

Sequential linked data: The state of affairs

Sequences are among the most important data structures in computer science. In the Semantic Web, however, little attention has been given to Sequential Linked Data. In previous work, we have discussed the data models that Knowledge Graphs commonly use for representing sequences and showed how these models have an impact on query performance and that this impact is invariant to triplestore implementations. However, the specific list operations that the management of Sequential Linked Data requires beyond the simple retrieval of an entire list or a range of its elements – e.g. to add or remove elements from a list –, and their impact in the various list data models, remain unclear. Covering this knowledge gap would be a significant step towards the realization of a Semantic Web list Application Programming Interface (API) that standardizes list manipulation and generalizes beyond specific data models. In order to address these challenges towards the realization of such an API, we build on our previous work in understanding the effects of various sequential data models for Knowledge Graphs, extending our benchmark and proposing a set of read-write Semantic Web list operations in SPARQL, with insert, update and delete support. To do so, we identify five classic list-based computer science sequential data structures (linked list, double linked list, stack, queue, and array), from which we derive nine atomic read-write operations for Semantic Web lists. We propose a SPARQL implementation of these operations with five typical RDF data models and compare their performance by executing them against six increasing dataset sizes and four different triplestores. In light of our results, we discuss the feasibility of our devised API and reflect on the state of affairs of Sequential Linked Data.

Preface to the MSCS Issue 31.1 (2021) Homotopy Type Theory and Univalent Foundations

This issue of Mathematical Structures in Computer Science is Part I of a Special Issue dedicated to the emerging field of Homotopy Type Theory and Univalent Foundations.

Practical concurrent unrolled linked lists using lazy synchronization

Linked lists and other list-based sets are some of the most ubiquitous data structures in computer science. They are useful in their own right and are frequently used as building blocks in other data structures. A linked list can be “unrolled” to combine multiple keys in each node; this improves storage density and overall performance. This organization also allows an operation to skip over nodes which cannot contain a key of interest. This work introduces a new high-performance concurrent unrolled linked list with a lazy synchronization strategy. Most write operations under this strategy can complete by locking a single node. Experiments show up to 300% improvement over other concurrent list-based sets.

Bidirectional Enhanced Selection Sort Algorithm Technique

Sorting algorithm refers to the arranging of numerical or alphabetical or character data in statistical order (ascending or descending). Sorting algorithm plays a vital role in searching and the field of data science. Most of the sorting algorithms with O(n2) time complexity are very efficient for a small list of elements. However, for large data, these algorithms are very inefficient. This study presented a remedy for the noted deficiencies of O(n2) sort algorithm for large data. Among the O(n2) algorithms, selection sort was the subject of the study considering its simplicity. Although selection sort is regarded as the most straightforward algorithm, it is also considered the second worst algorithm in terms of time complexity for large data. Several enhancements were conducted to address the inefficiencies of selection sort. However, the procedures presented in all the enhancements can still lead to some unnecessary comparisons, and iterations that cause poor sorting performance. The modified selection sort algorithm utilizes a Bidirectional Enhanced Selection Sort Algorithm Technique to reduce the number of comparisons and iterations that causes sorting delays. The modified algorithm was tested using varied data to validate the performance. The result was compared with the other O(n2) algorithm. The results show that the modified algorithm has a significant run time complexity improvement compared with the other O(n2) algorithms. This study has a significant contribution to the field of data structures in computer science and the field of data science.

Preface to special issue: ICTAC 2015

This issue of Mathematical Structures in Computer Science (MSCS) contains a selection of papers presented at the 12th International Colloquium on Theoretical Aspects of Computing (ICTAC 2015), which took place in Cali, Colombia, on October 29–31, 2015.

Reducing The Space And Time Complexity By The Use of Triangular Matrices

Matrisler bilgisayar bilimlerinde sıklıkla kullanılan veri yapılarıdır. Üçgensel matris gibi özel matris türleri için programlama dillerinde hazır yapılar bulunmamaktadır. Bir veri yapısı olarak üçgensel matris kullanmak gerekiyorsa programlama dilinden kaynaklanan bu eksiklik nedeniyle bellek ve zaman karmaşıklığı yönünden etkin olmayan yazılımlar kodlanmaktadır. Bu çalışmada üçgensel matris tipindeki yapıların bir boyutlu dizi olarak temsil edilmesinde kullanılan dönüşüm ve ters dönüşüm formülleri elde edilerek programların yer ve zaman karmaşıklığı açısından etkinliğinin arttırılması amaçlanmaktadır.

Automata Approach to XML Data Indexing

The internal structure of XML documents can be viewed as a tree. Trees are among the fundamental and well-studied data structures in computer science. They express a hierarchical structure and are widely used in many applications. This paper focuses on the problem of processing tree data structures; particularly, it studies the XML index problem. Although there exist many state-of-the-art methods, the XML index problem still belongs to the active research areas. However, existing methods usually lack clear references to a systematic approach to the standard theory of formal languages and automata. Therefore, we present some new methods solving the XML index problem using the automata theory. These methods are simple and allow one to efficiently process a small subset of XPath. Thus, having an XML data structure, our methods can be used efficiently as auxiliary data structures that enable answering a particular set of queries, e.g., XPath queries using any combination of the child and descendant-or-self axes. Given an XML tree model with n nodes, the searching phase uses the index, reads an input query of size m, finds the answer in time O ( m ) and does not depend on the size of the original XML document.

Preface

This special issue of Mathematical Structures in Computer Science is dedicated to the memory of Barry Cooper (October 9, 1943–October 26, 2015). Barry's life in research had a huge impact on the development of the world of computability. Aside from his enormous achievements in classical computability theory, he contributed immensely to the promotion of interdisciplinary developments related to computability, in particular, by founding the Association for Computability in Europe (CiE) and its annual, highly successful conference series.

On naturally continuous non-dcpo domains

After works of Normann and the author on sequentiality (Normann 2006Mathematical Structures in Computer Science16 (2) 279–289; Normann and Sazonov 2012Annals of Pure and Applied Logic163 (5) 575–603; Sazonov 2007Logical Methods in Computer Science3 (3:7) 1–50), the necessity and possibility of a non-dcpo domain theory became evident. In this paper, the category of continuous dcpo domains is generalized to a category of ‘naturally’ continuous non-dcpo domains with ‘naturally’ continuous maps as arrows. A full subcategory of the latter, assuming a kind of bounded-completeness requirement of domains and presence of ⊥ in each, proves to be Cartesian closed and equivalent to a subclass of Ershov's general A-spaces (Ershov 1974Algebra and Logics12 (4) 369–416). This extends a non-dcpo generalization of Scott (algebraic) domains introduced and proved to be equivalent to Ershov's general f-spaces (Ershov 1972Algebra and Logic11 (4) 367–437) in Sazonov (2007 op. cit.; 2009 Annals of Pure and Applied Logic159 (3) 341–355).The current approach to natural domains (v-domains) is different from f-spaces and A-spaces in that it has arisen in Sazonov (2007 op. cit.) in a different way from defining fully abstract models for some versions of the language PCF over Integers, whereas the Ershov's approach was not initially related with full abstraction, and non-dcpo version of f-spaces and A-spaces were originally considered in an abstract (mainly topological) style. In this paper devoted to naturally continuous natural domains (v-continuous v-domains), we also work in an abstract (mainly order-theoretic) style but with the hope to relate it in the future with the ideas of PCF over Reals by exploring and adapting the ideas in Escardó (1996Theoretical Computer Science162 (1) 79–115), Escardó et al. (2004Mathematical Structures in Computer Science, 14 (6), Cambridge University Press 803–814), Marcial-Romero and Escardó (2007Theoretical Computer Science379 (1-2) 120–141), Sazonov (2007 op. cit.).

Preface to the special issue: Continuity, computability, constructivity: from logic to algorithms 2013

This issue of Mathematical Structures in Computer Science is composed mainly of papers submitted by participants of the Workshop ‘Continuity, Computability, Constructivity: From Logic to Algorithms,’ held in Gregynog, a conference centre of the University of Wales located in the beautiful nature of Mid Wales, in the last week of June 2013. In addition, several colleagues accepted our invitation to contribute to this volume.

A second note on the feasibility of generalized universal composability

Yao et al. (A note on the feasibility of generalized universal composability.Theory and Applications of Models of Computationpp. 474–485, 2007; A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science,19(1), pp. 193–205) claimed a potential limitation on the class of protocols that could be securely implemented in the generalized universal composability (GUC) framework proposed by Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Specifically, Yao et al. presented a concrete attack on a GUC Zero Knowledge (GUCZK) protocol, a natural adaptation Blum's ZK proof for Directed Hamiltonicity using the general GUC feasibility of Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Interestingly, the attack was not analysed in the GUC model in Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) but in theFUC model, a new UC-like framework proposed in the same work. Nonetheless, Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) argued that, in light of this attack, GUC would lose its concurrent general composability and proof of knowledge properties. Concretely, they argue that GUC composability would now be with respect to some adversaries with limited access to external arbitrary protocols.In this work, we show that the claimed attack from Yao et al. is indeed harmless and does not contradict the security of the mentioned GUCZK protocol, thus restoring the general feasibility for GUC.

Foreword: special issue on coalgebraic logic

The second Dagstuhl seminar on coalgebraic logics took place from October 7–12, 2012, in the Leibniz Forschungszentrum Schloss Dagstuhl, following a successful earlier one in December 2009. From the 44 researchers who attended and the 30 talks presented, this collection highlights some of the progress that has been made in the field. We are grateful to Giuseppe Longo and his interest in a special issue in Mathematical Structures in Computer Science.

Classical realizability and arithmetical formulæ

In this paper, we treat the specification problem in Krivine classical realizability (Krivine 2009Panoramas et synthèses27), in the case of arithmetical formulæ. In the continuity of previous works from Miquel and the first author (Guillermo 2008Jeux de réalisabilité en arithmétique classique, Ph.D. thesis, Université Paris 7; Guillermo and Miquel 2014Mathematical Structures in Computer Science, Epub ahead of print), we characterize the universal realizers of a formula as being the winning strategies for a game (defined according to the formula). In the first sections, we recall the definition of classical realizability, as well as a few technical results. In Section 5, we introduce in more details the specification problem and the intuition of the game-theoretic point of view we adopt later. We first present a game1, that we prove to be adequate and complete if the language contains no instructions ‘quote’ (Krivine 2003Theoretical Computer Science308259–276), using interaction constants to do substitution over execution threads. We then show that as soon as the language contain ‘Quote,’ the game is no more complete, and present a second game2that is both adequate and complete in the general case. In the last Section, we draw attention to a model-theoretic point of view and use our specification result to show that arithmetical formulæ are absolute for realizability models.

Preface

This special issue of Mathematical Structures in Computer Science is devoted to the fourteenth Italian Conference on Theoretical Computer Science (ICTCS) held at University of Palermo, Italy, from 9th to 11th September 2013. ICTCS is the conference of the Italian Chapter of the European Association for Theoretical Computer Science and covers a wide spectrum of topics in Theoretical Computer Science, ranging from computational complexity to logic, from algorithms and data structure to programming languages, from combinatorics on words to distributed computing. For this reason, the contributions here included come from very different areas of Theoretical Computer Science. In fact this special issue is motivated by the desire to give people who have presented their ideas at the 14th ICTCS the opportunity to publish papers on their work. Submitted papers have been subject to a careful and severe reviewing process and 11 of them were selected for this special issue.

A Knowledge of Metrics on Analysis of Social Graphs

Graph based data mining has become quite popular in the last few years. One of the best studied data structures in computer science and discrete mathematics are graphs. The use of social media has grown significantly in recent years. With the growth in its use, there has also been a substantial growth in the amount of information generated by users of social media. This paper discusses the metrics which are used in mining of social graphs. Keywords: Data Mining, Graphs, Social Graphs

Preface to special issue: EXPRESS 2011

This issue of Mathematical Structures in Computer Science contains a selection of papers presented at the 18th International Workshop on Expressiveness in Concurrency (EXPRESS'11), a satellite event of CONCUR'11, held on September 5th, 2011 in Aachen, Germany.

Preface to the special issue: Computing with infinite data: topological and logical foundations

This special issue of Mathematical Structures in Computer Science is composed mainly of papers submitted by participants of the Dagstuhl Seminar on Computing with Infinite Data: Topological and Logical Foundations. The workshop took place in the Schloss Dagstuhl - Leibniz Center for Informatics in the first half of October 2011.