We consider approximability of two optimization problems called Minimum Open k-Monopoly (Min-Open-k-Monopoly) and Minimum Partial Open k-Monopoly (Min-P-Open-k-Monopoly), where k is a fixed positive integer. The objective, in Min-Open-k-Monopoly, is to find a minimum cardinality vertex set \(S \subseteq V\) in a given graph G = (V,E) such that \(|N(v) \cap S| \geq \frac {1}{2} |N(v)| + k\), for every

We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions F and a Boolean function f, determine if f is in the clone generated by F, i.e., if it can be expressed by a circuit with F-gates. Here, f and elements of F are given as circuits or formulas over the usual De Morgan basis. Böhler and Schnoor (Theory Comput. Syst. 41(4):753–777, 2007) proved

The concept of Reload cost in a graph refers to the cost that occurs while traversing a vertex via two of its incident edges. This cost is uniquely determined by the colors of the two edges. This concept has various applications in transportation networks, communication networks, and energy distribution networks. Various problems using this model are defined and studied in the literature. The problem

Set Cover is one of the well-known classical NP-hard problems. We study the conflict-free version of the Set Cover problem. Here we have a universe \(\mathcal {U}\), a family \(\mathcal {F}\) of subsets of \(\mathcal {U}\) and a graph \(G_{\mathcal {F}}\) on the vertex set \(\mathcal {F}\) and we look for a subfamily \(\mathcal {F}^{\prime } \subseteq \mathcal {F}\) of minimum size that covers \(\mathcal

A Correction to this paper has been published: https://doi.org/10.1007/s00224-020-10020-x

We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6(3), 14:1–14:17 2019) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance ms per round for each server. The costs are measured similarly to

A word x that is absent from a word y is called minimal if all its proper factors occur in y. Given a collection of k words y1, … , yk over an alphabet Σ, we are asked to compute the set \(\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}\) of minimal absent words of length at most ℓ of the collection {y1, … , yk}. The set \(\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}\) contains all the words x such that x is

Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph G can be defined with help of a chip firing game on G. The stable divisorial gonality of G is the minimum divisorial gonality over all subdivisions of edges of G. In this paper we prove that deciding whether a given connected graph has stable

We examine conditions under which a semicomputable set in a computable topological space is computable. In particular, we examine topological pairs (A, B) with the following property: if X is a computable topological space and \(f:A\rightarrow X\) is an embedding such that f(A) and f(B) are semicomputable sets in X, then f(A) is a computable set in X. Such pairs (A, B) are said to have computable type

In the smallest grammar problem, we are given a word w and we want to compute a preferably small context-free grammar G for the singleton language {w} (where the size of a grammar is the sum of the sizes of its rules, and the size of a rule is measured by the length of its right side). It is known that, for unbounded alphabets, the decision variant of this problem is NP-hard and the optimisation variant

Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases, but have been less well-studied when the volume of the input is truly massive, and cannot even be read into memory. This is captured by the streaming model of computation

We consider the list-coloring problem from the perspective of parameterized complexity. In the classical graph coloring problem we are given an undirected graph and the goal is to color the vertices of the graph with minimum number of colors so that end points of each edge get different colors. In list-coloring, each vertex is given a list of allowed colors with which it can be colored. An interesting

Given a database of vectors, a cosine threshold query returns all vectors in the database having cosine similarity to a query vector above a given threshold θ. These queries arise naturally in many applications, such as document retrieval, image search, and mass spectrometry. The paper considers the efficient evaluation of such queries, as well as of the closely related top-k cosine similarity queries

In the Cluster Vertex Deletion problem the input is a graph G and an integer k. The goal is to decide whether there is a set of vertices S of size at most k such that the deletion of the vertices of S from G results in a graph in which every connected component is a clique. We give an algorithm for Cluster Vertex Deletion whose running time is O∗(1.811k).

We investigate scheduling algorithms for distributed transactional memory systems where transactions residing at nodes of a communication graph operate on shared, mobile objects. A transaction requests the objects it needs, executes once those objects have been assembled, and then possibly forwards those objects to other waiting transactions. Minimizing execution time in this model is known to be NP-hard

The isomorphism problem for groups, when the groups are given by their Cayley tables is a well-studied problem. This problem has been studied for various restricted classes of groups. Kavitha gave a linear time isomorphism algorithm for abelian groups (JCSS 2007). Although there are isomorphism algorithms for certain nonabelian group classes represented by their Cayley tables, the complexities of those

We show that any nondeterministic read-once branching program that decides a satisfiable Tseitin formula based on an n × n grid graph has size at least 2Ω(n). Then using the Excluded Grid Theorem by Robertson and Seymour we show that for an arbitrary graph G(V, E) any nondeterministic read-once branching program that computes a satisfiable Tseitin formula based on G has size at least \(2^{\Omega (\text

There is a long tradition in understanding graphs by investigating their adjacency matrices by means of linear algebra. Similarly, logic-based graph query languages are commonly used to explore graph properties. In this paper, we bridge these two approaches by regarding linear algebra as a graph query language. More specifically, we consider MATLANG, a matrix query language recently introduced, in

We investigate the complexity of the containment problem “Does \(L(\mathcal {A})\subseteq L({\mathscr{B}})\) hold?” for register automata and timed automata, where \({\mathscr{B}}\) is assumed to be unambiguous and \(\mathcal {A}\) is arbitrary. We prove that the problem is decidable in the case of register automata over \((\mathbb N,=)\), in the case of register automata over \((\mathbb Q,<)\) when

The Minimum Circuit Size Problem (MCSP) has been the focus of intense study recently; MCSP is hard for SZK under rather powerful reductions (Allender and Das Inf. Comput. 256, 2–8, 2017), and is provably not hard under “local” reductions computable in TIME(n0.49) (Murray and Williams Theory Comput. 13(1), 1–22, 2017). The question of whether MCSP is NP-hard (or indeed, hard even for small subclasses

We study the complexity of evaluating well-designed pattern trees, a query language extending conjunctive queries with the possibility to define parts of the query to be optional. This possibility of optional parts is important for obtaining meaningful results over incomplete data sources as it is common in semantic web settings. Recently, a structural characterization of the classes of well-designed

As the modern integrated circuit continues to grow in complexity, the design of very large-scale integrated (VLSI) circuits involves massive teams employing state-of-the-art computer-aided design (CAD) tools. An old yet significant CAD problem for VLSI circuits is physical design automation. In physical design automation, we need to compute the best physical layout of millions to billions of circuit

Structured d-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs are restricted structured d-DNNFs. Beame and Liew (2015) as well as Bova and Szeider (2017) mentioned the question whether structured d-DNNFs are really more general

The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input database? In view of the fact that this problem is undecidable, it is natural to ask whether known well-behaved

In the sliding window streaming model the goal is to compute an output value that only depends on the last n symbols from the data stream. Thereby, only space sublinear in the window size n should be used. Quite often randomization is used in order to achieve this goal. In the literature, one finds two different correctness criteria for randomized sliding window algorithms: (i) one can require that

We give two different proofs of the fact that non-oblivious selection via regular group sets preserves normality. Non-oblivious here means that whether or not a symbol is selected can depend on the symbol itself. One proof relies on the incompressibility of normal sequences, the other on the use of augmented dynamical systems.

We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely constantly connected dynamic graphs. This problem has already been studied in the case where the agent knows the dynamics of the graph and the underlying graph is a ring of n vertices (Ilcinkas and Wade 2018). In this paper, we consider the same problem and we suppose that the underlying graph is a

This paper is dedicated to studying decidability properties of theories of regular languages with classical operations: union, concatenation, and the Kleene star. The theory with union only is a theory of some Boolean algebra, so it is decidable. We prove that the theory of regular languages with the Kleene star only is decidable. If we use union and concatenation simultaneously, then the theory becomes

Two points p and q in a simple polygon P are k-visible when the line segment pq crosses the boundary of P at most k times. Given a query point q, a positive integer k, and a polygon P, we design an algorithm that computes the region of P that is k-visible from q in O(nk) time, where n denotes the number of vertices of P. This region is called the k-visibility region of q. This is the first algorithm

The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink. In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink. In a preliminary version of this paper, we provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges

Many shared memory algorithms have to deal with the problem of determining whether the value of a shared object has changed in between two successive accesses of that object by a process when the responses from both are the same. Motivated by this problem, we define the signal detection problem, which can be studied on a purely combinatorial level. Consider a system with n + 1 processes consisting

MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting algorithm which, up to today, for many input sizes achieves the best known upper bound on the number of comparisons. Indeed, it gets extremely close to the information-theoretic lower bound. While the worst-case behavior is well understood, only little is known about the average case. This work takes a closer look at the average

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database

We revisitself-adjustingexternal memory tree data structures, which combine the optimal (and practical) worst-case I/O performances of B-trees, while adapting to the online distribution of queries. Our approach is analogous to undergoing efforts in the BST model, where Tango Trees (Demaine et al., SIAM J. Comput. 37(1), 240–251, 2007) were shown to be \(O(\log \log N)\)-competitive with the runtime

Huffman coding is known to be optimal, yet its dynamic version may yield smaller compressed files. The best known bound is that the number of bits used by dynamic Huffman coding in order to encode a message of n characters is at most larger by n bits than the size of the file required by static Huffman coding. In particular, dynamic Huffman coding can also generate a larger encoded file than the static

Holant problems are a general framework to study counting problems. Both counting constraint satisfaction problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for \(\text {Holant}^{*}(\mathcal {F})\), where \({\mathcal {F}}\) is a set of constraint functions on Boolean variables and taking complex values. The constraint functions need not be symmetric functions

We study the computation of revenue-maximizing envy-free outcomes, in a monopoly market with budgeted buyers. Departing from previous works, we focus on buyers with combinatorial valuation functions, that are defined over subsets of distinct goods. Our results concern several classes of valuation functions. For single-minded budgeted buyers, we show a best possible polynomial-time approximation of

For a graph G = (V, E) with no isolated vertices, a set \(D\subseteq V\) is called a semipaired dominating set of G if (i)D is a dominating set of G, and (ii)D can be partitioned into two element subsets such that the vertices in each two element set are at distance at most two. The minimum cardinality of a semipaired dominating set of G is called the semipaired domination number of G, and is denoted

We investigate parameterized algorithms for the NP-hard problem Min-Power Asymmetric Connectivity (MinPAC) that has applications in wireless sensor networks. Given a directed arc-weighted graph, MinPAC asks for a strongly connected spanning subgraph minimizing the summed vertex costs. Here, the cost of each vertex is the weight of its heaviest outgoing arc in the chosen subgraph. We present linear-time

This article presents a new multiplication algorithm based on the Collatz function. Assuming the validity of the Collatz conjecture, the time complexity of multiplying two n-digit numbers is O(kn), where the k is the number of odd steps in the Collatz trajectory of the first multiplicand. Most likely, the algorithm is only of theoretical interest.

For a string S, a palindromic substring S[i..j] is said to be a shortest unique palindromic substring (SUPS) for an interval [s,t] in S, if S[i..j] occurs exactly once in S, the interval [i,j] contains [s,t], and every palindromic substring containing [s,t] which is shorter than S[i..j] occurs at least twice in S. In this paper, we study the problem of answering SUPS queries on run-length encoded strings

Given a set A of n people, with each person having a preference list that ranks a subset of A as his/her acceptable partners in order of preference, we consider the Roommates Problem (rp) and the Marriage Problem (mp) of matching people with their partners. In rp there is no further restriction, while in mp only people of opposite genders can be acceptable partners. For a pair of matchings X and Y

We study the Independent Feedback Vertex Set problem — a variant of the classic Feedback Vertex Set problem where, given a graph G and an integer k, the problem is to decide whether there exists a vertex set \(S\subseteq V(G)\) such that G ∖ S is a forest and S is an independent set of size at most k. We present an \(\mathcal {O}^{\ast }((1+\varphi ^{2})^{k})\)-time FPT algorithm for this problem,

The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i’th bit on the previousi − 1 bits is limited for every i ∈ [n]. If the dependence of the i’th bit on the remainingn − 1 bits is limited, then this is a strongSV-source. Even the strong SV -sources are known not to admit (universal) deterministic extractors, but

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair (u, v) of d-ary cube-free words, if u can be infinitely extended to the right and v can be infinitely extended to the left respecting the cube-freeness property, then there exists a “transition” word w over the same alphabet such that uwv is cube free. The crucial case is the

We study automatic equivalence and nested equivalence structures. The goal is to compare and contrast these automatic structures with computable equivalence and nested equivalence structures. Equivalence structures \(\mathcal {A}\) may be characterized by their characters \(\chi ({\mathcal {A}})\) which encodes the number of equivalence classes of any given size. The characters of computably categorical

We strengthen a result by Laskar and Lyle (Discrete Appl. Math. 157, 330–338 2009) by proving that it is NP-complete to decide whether a bipartite planar graph can be partitioned into three independent dominating sets. In contrast, we show that this is always possible for every maximal outerplanar graph with at least three vertices. Moreover, we extend their previous result by proving that deciding

In the Maximum Connectivity Improvement (MCI) problem, we are given a directed graph G = (V,E) and an integer B and we are asked to find B new edges to be added to G in order to maximize the number of connected pairs of vertices in the resulting graph. The MCI problem has been studied from the approximation point of view. In this paper, we approach it from the parameterized complexity perspective in

Orbit Problems are a class of fundamental reachability questions that arise in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. Instances of the problem comprise a dimension \(d\in \mathbb {N}\), a square matrix \(A\in \mathbb {Q}^{d\times d}\), and a query regarding the behaviour of some sets under repeated applications

Let π be a family of graphs. In the classical π-Vertex Deletion problem, given a graph G and a positive integer k, the objective is to check whether there exists a subset S of at most k vertices such that G − S is in π. In this paper, we introduce the conflict free version of this classical problem, namely Conflict Free π-Vertex Deletion (CF-π-VD), and study this problem from the viewpoint of classical

The original version of the article was inadvertently published with misinterpretations on author’s proof corrections on mathematical expressions.

We study the problem of computing a longest increasing subsequence in a sequence S of n distinct elements in the presence of persistent comparison errors. In this model, Braverman and Mossel (Noisy sorting without resampling, SODA 2008, pages 268–276, 2008) every comparison between two elements can return the wrong result with some fixed (small) probability p, and comparisons cannot be repeated. Computing

We study the problem of finding a minimum weight connected subgraph spanning at least k vertices on planar, node-weighted graphs. We give a (4 + ε)-approximation algorithm for this problem. We achieve this by utilizing the recent Lagrangian-multiplier preserving (LMP) primal-dual 3-approximation for the node-weighted prize-collecting Steiner tree problem by Byrka et al. (SWAT’16) and adopting an approach

The article title in the original publication contains an error. The correct title is presented in this Erratum. The online version of the original article can be found at: https://doi.org/10.1007/s00224-019-09930-2

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: first, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not

We consider the online Minimum-Cost Perfect Matching with Delays (MPMD) problem introduced by Emek et al. (STOC 2016), in which a general metric space is given, and requests for points in space are submitted in different times in this space by an adversary. The goal is to match requests, while minimizing the sum of distances between matched pairs in addition to the time intervals passed from the moment

As a variant of the equal entropy cover problem, we ask whether all multidimensional sofic shifts with countably many configurations have SFT covers with countably many configurations. We answer this question in the negative by presenting explicit counterexamples. We formulate necessary conditions for a vertically periodic shift space to have a countable SFT cover, and prove that they are sufficient

We investigate pure Nash equilibria in generalized graphk-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges {v, u} incident to v such

We investigate the problem of detecting periodic trends within a string S of length n, arriving in the streaming model, containing at most k wildcard characters, where k = o(n). A wildcard character is a special character that can be assigned any other character. We say that S has wildcard-period p if there exists an assignment to each of the wildcard characters so that in the resulting stream the

Stable and balanced outcomes of network bargaining games have been investigated recently, but the existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem have integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident