A graph G=(V,E) is δ-hyperbolic if for any four vertices u,v,w,x, the two larger of the three distance sums d(u,v)+d(w,x), d(u,w)+d(v,x), d(u,x)+d(v,w) differ by at most 2δ≥0. This paper describes the eccentricity terrain of a δ-hyperbolic graph. The eccentricity function eG(v)=max⁡{d(v,u):u∈V} partitions vertices of G into eccentricity layers Ck(G)={v∈V:eG(v)=rad(G)+k}, k∈N, where rad(G)=min⁡{eG(v):v∈V}

We investigate a distributed maximal independent set reconfiguration problem, in which there are two MIS for which every node is given its membership status, and the nodes need to communicate with their neighbors to find a reconfiguration schedule from the first MIS to the second. We forbid two neighbors to change their membership status at the same step. We provide efficient solutions when the intermediate

Bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k≥2, items having sizes in (0,1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem and prove a lower bound of 2 on the overall asymptotic

Probabilistic bisimilarity, due to Segala and Lynch, is an equivalence relation that captures which states of a probabilistic automaton behave exactly the same. Deng et al.proposed a robust quantitative generalization of probabilistic bisimilarity. Their probabilistic bisimilarity distances of states of a probabilistic automaton capture the similarity of their behaviour. The smaller the distance, the

We show that structures with only one binary function symbol are universal for “online” (punctual) computable structures. In contrast, we give a description of punctually categorical graphs which implies that graphs are not universal for online computability.

The task of aggregating individual judgments over logically interconnected propositions is called judgment aggregation. Manipulation of judgment aggregation procedures has first been studied by List [45] and Dietrich and List [27], and Endriss et al. [30] were the first to study it from a computational perspective. Baumeister et al. [7] extended their results on manipulation and introduced the concept

We consider threshold group testing – a generalization of group testing, which asks to identify a set of positive individuals in a population, by performing tests on pools of elements. Each test is represented by a subset Q of individuals and its output is yes if Q contains at least one positive element and no otherwise. Threshold group testing is the natural generalization, introduced by P. Damaschke

We study the computational power of parsing expression grammars (PEGs). We begin by constructing PEGs with unexpected behaviour, and surprising new examples of languages with PEGs, including the language of palindromes whose length is a power of two, and a binary-counting language. We then propose a new computational model, the scaffolding automaton, and prove that it exactly characterises the computational

Given a range space (X,R), where X is a set equipped with probability measure P, R ⊂ 2X is a family of measurable subsets, and ε>0, an ε-net is a subset of X in the support of P, which intersects each R ∈ R with P(R) ≥ε. In many situations the size of ε-nets depends on ε and on natural complexity measures. The aim of this paper is to give a systematic treatment of such complexity measures arising in

A strict connection tree of a graph G for a set W is a tree subgraph of G whose leaf set equals W. The Strict terminal connection problem (S-TCP) is a network design problem whose goal is to decide whether G admits a strict connection tree T for W with at most ℓ vertices of degree 2 and r vertices of degree at least 3. We establish a Poly vs. NP-c dichotomy for S-TCP with respect to ℓ and Δ(G). We

Elementary net systems (ENS) are the most fundamental class of Petri nets. Given a labeled transition system (TS) A, feasibility is the NP-complete decision problem whether A can be synthesized into an ENS. We analyze the impact of state degree, the number of allowed successors and predecessors of states in A, and event manifoldness, the amount of occurrences that an event can have in A, on the computational

Similar to the satisfiability (SAT) problem, which can be seen to be the archetypical problem for NP, the quantified Boolean formula problem (QBF) is the archetypical problem for PSPACE. Recently, Atserias and Oliva (2014) showed that, unlike for SAT, many of the well-known decompositional parameters (such as treewidth and pathwidth) do not allow efficient algorithms for QBF. The main reason for this

Edge connectivity is a crucial measure of the robustness of a network. Several edge connectivity variants have been proposed for measuring the reliability and fault tolerance of networks under various conditions. Let G be a connected graph, S be a subset of edges in G, and k be a positive integer. If G−S is disconnected and every component has at least k vertices, then S is a k-extra edge-cut of G

Stellar datacenter networks are a recent generic construction designed to transform a base-graph into a dual-port, server-centric datacenter network. We prove that the S-bisection width of any stellar datacenter network can be obtained from the solution of isoperimetric problems on the base-graph, provided that the base-graph is regular. We extend previous research on the stellar datacenter networks

We focus on the computational complexity of regular simple path queries (RSPQs). We consider the following problem RSPQ(L) for a regular language L: given an edge-labeled digraph G and two nodes x and y, is there a simple path from x to y that forms a word belonging to L? We fully characterize the frontier between tractability and intractability for RSPQ(L). More precisely, we prove RSPQ(L) is either

Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by lowness notions from computability theory, Allender introduced the concept of “low for speed” oracles. An oracle A is low for speed if relativizing to A has essentially no effect on computational complexity, meaning that if

We obtain a complete classification of graphs H for which the class of (triangle,H)-free graphs is well-quasi-ordered by the induced subgraph relation and an almost complete classification of graphs H for which the class of (triangle,H)-free graphs has bounded clique-width. In particular, we show that for these graph classes, well-quasi-orderability implies boundedness of clique-width. To obtain our

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k≥2. This corrects a claim in the literature that the Tucker search problem is in PPAD.

We study the derivational complexity of context-free and context-sensitive grammars by counting the maximal number of non-regular and non-context-free rules used in a derivation, respectively. The degree of non-regularity/non-context-freeness of a language is the minimum degree of non-regularity/non-context-freeness of context-free/context-sensitive grammars generating it. A language has finite degree

Truth Discovery is an important learning problem arising in data analytics related fields. It concerns about finding the most trustworthy information from a dataset acquired from a number of unreliable sources. The problem has been extensively studied and a number of techniques have already been proposed. However, all of them are of heuristic nature and do not have any quality guarantee. In this paper

We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We consider the probabilistic questions of computing the expected value and the cumulative distribution for such random variables. The exact answers to the probabilistic

We consider subexponential algorithms finding weighted homomorphisms from intersection graphs of curves (string graphs) with n vertices to a fixed graph H. We provide a complete dichotomy: if H has no two vertices sharing two common neighbors, then the problem can be solved in time 2O(n2/3log⁡n), otherwise there is no subexponential algorithm, assuming the ETH. Then we consider locally constrained

We analyse the complexity of approximate counting constraint satisfactions problems #CSP(F), where F is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is known if F contains arbitrary unary functions. We strengthen this result by fixing any permissive strictly increasing unary function and any permissive strictly decreasing unary function, and requiring

For a finite fixed collection of graphs F, the F-M-Deletion problem consists in, given a graph G and an integer k, decide whether there exists S⊆V(G) with |S|≤k such that G∖S does not contain any of the graphs in F as a minor. We provide lower bounds under the ETH on the smallest function fF such that F-M-Deletion can be solved in time fF(tw)⋅nO(1) on n-vertex graphs, where tw denotes the treewidth

The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by finite sets of labelled rules that rewrite roots of first-order terms. The framework is equivalent to PDA where also deterministic (i.e. alternative-free) epsilon-steps

Consider a finite set A and n≥1. We study complete simulation of transformations of An, also known as automata networks. For m≥n, a transformation of Am is n-complete of size m if it may simulate every transformation of An by updating one register at a time. Using tools from memoryless computation, we establish that there is no n-complete transformation of size n, but there is one of size n+1. By studying

In the Graph bipartization (or Odd Cycle Transversal) problem, the objective is to decide whether a given graph G can be made bipartite by the deletion of k vertices for some given k. The parameterized complexity of Odd Cycle Transversal was resolved in the breakthrough paper of Reed, Smith and Vetta [Operations Research Letters, 2004], who developed an algorithm running in time O(3kkmn). The question

Here we study cooperating distributed systems (CD-systems) of restarting automata that are very restricted: they are deterministic, they cannot rewrite, but only delete symbols, they restart immediately after performing a delete operation, they are stateless, and they have a read/write window of size 1 only, that is, these are stateless deterministic R(1)-automata. We study the expressive power of

Given a boolean n × n matrix A we consider arithmetic circuits for computing the transformation x ↦ Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on separating OR-circuits from the two other models in terms of circuit complexity: We show

We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide

We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact