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

We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most m-k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most m-k arcs. We show that (i) Directed Multiplicative Spanner admits a polynomial kernel of size mathcal {O}(k^4t^5) and can be solved in randomized (4t)^kcdot n^{mathcal {O}(1)} time, (ii) the weighted variant of Directed Multiplicative Spanner can be solved in k^{2k}cdot n^{mathcal {O}(1)} time on directed acyclic graphs, (iii) Directed Additive Spanner is {{,mathrm{mathsf{W}},}}[1]-hard when parameterized by k for every fixed tge 1 even when the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is {{,mathrm{mathsf{FPT}},}} when parameterized by t and k.

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.

The aim of this paper is to give an introduction how to use categorical methods in a specific field of computer science: The field of high-level-replacement systems has its roots in the well-established theories of formal languages, term rewriting, Petri nets, and graph grammars playing a fundamental role in computer science. More precisely, it is a generalization of the algebraic approach to graph grammars which is based on gluing constructions for graphs defined as pushouts in the category of graphs. The categorical theory of high-level-replacement systems is suitable for the dynamic handling of a large variety of high-level structures in computer science including different kinds of graphs and algebraic specifications. In this paper we discuss the basic principles and techniques from category theory applied in the field of high-level-replacement systems and present some basic results together with the corresponding categorical proof techniques.

The scope of computation has expanded dramatically beyond the rubric of discrete, deterministic sequential computation under which it has been studied for many decades. That focus, of course, led to a great deal of deep and beautiful theory, but our focus in this special issue of Mathematical Structures in Computer Science is on new directions that have emerged from the study of computational phenomena in other settings, and thus on a celebration of the diversity of ideas, methods, new applications and novel sources of inspiration that have marked the modern era. The papers in this issue come from sources extending far beyond the core of computer science, yet using many of the central ideas that have evolved within computer science and mathematics. The nexus of all this activity has been, on the one hand, the boundary between logic and computation, and, on the other hand, the natural sciences, particularly physics and biology. The papers in this collection are expanded versions of selected papers from the DCM 2010 workshop, which was held in Edinburgh in July 2010. The theme of the workshop was Causality, Computation and Physics.

Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected (resp., 2-vertex-connected) if the removal of any edge (resp., vertex) leaves the graph strongly connected. In this paper we present improved algorithms for computing the maximal 2-edge- and 2-vertex-connected subgraphs of a given directed graph. These problems were first studied more than 35 years ago, with O(mn) time algorithms for graphs with m edges and n vertices being known since the late 1980s. In contrast, the same problems for undirected graphs are known to be solvable in linear time. Henzinger et al. [ICALP 2015] recently introduced O(n2) time algorithms for the directed case, thus improving the running times for dense graphs. Our new algorithms run in time O(m3/2), which further improves the running times for sparse graphs.The notion of 2-connectivity naturally generalizes to k-connectivity for k > 2. For constant values of k, we extend one of our algorithms to compute the maximal k-edge-connected in time O(m3/2 log n), improving again for sparse graphs the best known algorithm by Henzinger et al. [ICALP 2015] that runs in O(n2 log n) time.

Automata Games for Multiple-model Checking

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

This special issue of Mathematical Structures in Computer Science contains a selection of papers presented at three satellite events of CONCUR'09, which was held between 31 August and 5 September 2009 in Bologna (Italy). Specifically, it contains three papers from the 16th International Workshop on Expressiveness in Concurrency (EXPRESS'09), one paper from the 2nd Interaction and Concurrency Experience (ICE'09) and two papers from the 6th Workshop on Structural Operational Semantics (SOS'09).

Grammars are fundamental structures in computer science that also have many applications in procedural content generation. This chapter starts by describing a classic type of grammar, the L-system, and its application to generating plants of various types. It then describes how rules and axioms for L-systems can be created through search-based methods. But grammars are not only useful for plants. Two longer examples discuss the generation of action-adventure levels through graph grammars, and the generation of Super Mario Bros. levels through grammatical evolution.

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.

The linear-probing hash table is one of the oldest and most widely used data structures in computer science. However, linear probing famously comes with a major draw-back: as soon as the hash table reaches a high memory utilization, elements within the hash table begin to cluster together, causing insertions to become slow. This phenomenon, now known as primary clustering, was first captured by Donald Knuth in 1963; at a load factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> , the expected time per insertion is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x^{2})$</tex> , rather than the more desirable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x)$</tex> . We show that there is more to the story than the classic analysis would seem to suggest. It turns out that small design decisions in how deletions are implemented have dramatic effects on the asymptotic performance of insertions. If these design decisions are made correctly, then even a hash table that is continuously at a load factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-\Theta(1/x)$</tex> can achieve average insertion time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{O}(x)$</tex> . A key insight is that the tombstones left behind by deletions cause a surprisingly strong “anti-clustering” effect, and that when insertions and deletions are one-for-one, the anti-clustering effects of deletions actually overpower the clustering effects of insertions. We also present a new variant of linear probing, which we call graveyard hashing, that completely eliminates primary clustering on any sequence of operations. If, when an operation is performed, the current load factor is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> for some <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex> , then the expected cost of the operation is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(x)$</tex> . One corollary is that, in the external-memory model with a data block size of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$B$</tex> , graveyard hashing offers the following remarkable guarantee: at any load factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> satisfying <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x=o(B)$</tex> , graveyard hashing achieves <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 +o(1)$</tex> expected block transfers per operation. Past external-memory hash tables have only been able to offer a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 +o(1)$</tex> guarantee when the block size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$B$</tex> is at least <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Omega(x^{2})$</tex> . Our results come with actionable lessons for both theoreticians and practitioners, in particular, that well-designed use of tombstones can completely change the asymptotic landscape of how the linear probing behaves (and if there are no deletions).

There are various logic-based approaches to modelling concurrent programming. The use of logic for system development concerns both the specification step and the study of the operational aspects (through proof analysis and construction) of such development. This means that we have to consider different logical systems for different uses of logic. Moreover, we can also consider concurrency from both points of view: we want to reason and to specify systems where some concurrency aspects are involved, but also to have some operational interpretation of concurrency within logic (focusing on the concept of proof). For this purpose, it seems clear that we have to identify and to study, on the one hand, the role and the treatment of objects (representation, inheritance, modularity, communication, and so on) in this context, and, on the other hand, the interaction of work on proofs and concurrency with the Object-Oriented Programming paradigm.The ECOOP’96 workshop on ‘Proof Theory of Concurrent Object-Oriented Programming’ took place in Linz, Austria, in July 1996. Its objective was to provide an integrated forum for the presentation of research and the exchange of ideas and experiences in the topics concerned with proofs, concurrency and object-oriented programming (specification, proof development, and so on). The call for papers for this Special Issue of Mathematical Structures in Computer Science can be considered to have been a natural scientific continuation of the workshop.The papers selected for this Special Issue address some of the topics discussed in the workshop. They present different alternative frameworks that are effectively based on a proof-theoretic approach. They illustrate, from different points of view, the interest, potentialities and difficulties of dealing with such an approach in the design of object-based concurrent systems.

Tries and PATRICIA tries are fundamental data structures in computer science with numerous applications. In a recent paper, a general framework for obtaining the mean and variance of additive shape parameters of tries and PATRICIA tries under the Bernoulli model was proposed. In this note, we show that a slight modification of this framework yields a central limit theorem for shape parameters, too. This central limit theorem contains many of the previous central limit theorems from the literature and it can be used to prove recent conjectures and derive new results. As an example, we will consider a refinement of the size of tries and PATRICIA tries, namely, the number of nodes of fixed outdegree and obtain (univariate and bivariate) central limit theorems. Moreover, trivariate central limit theorems for size, internal path length and internal Wiener index of tries and PATRICIA tries are derived as well.

The chapter provides a comprehensive and in-depth exploration of two fundamental linear data structures in computer science: Stack and Queue. It begins with an introduction to these data structures, highlighting their key features and fundamental differences. It then explains various operations that can be performed on both data structures, such as push, pop, enqueue, and dequeue. These implementations are thoroughly compared and contrasted, highlighting their advantages and disadvantages. These applications are discussed in detail, showcasing the versatility of Stack and Queue data structures in different scenarios. The chapter includes Python code snippets demonstrating Stack and Queue data structures further to aid the reader's understanding of the material. This chapter provides a comprehensive and practical guide to Stack and Queue data structures, making it a valuable resource for computer science students, researchers, and practitioners.

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.