The b-Exact Multicover problem takes a universe U of n elements, a family \(\mathcal {F}\) of m subsets of U, a function \({\textsf {dem}}: U \rightarrow \{1,\ldots ,b\}\) and a positive integer k, and decides whether there exists a subfamily(set cover) \(\mathcal {F}^{\prime }\) of size at most k such that each element u ∈ U is covered by exactly dem(u) sets of \(\mathcal {F}^{\prime }\). The b-Exact

Let \({\mathbb {F}}[X]\) be the polynomial ring in the variables X = {x1,x2,…,xn} over a field \({\mathbb {F}}\). An ideal I = 〈p1(x1),…,pn(xn)〉 generated by univariate polynomials \(\{p_{i}(x_{i})\}_{i=1}^{n}\) is a univariate ideal. Motivated by Alon’s Combinatorial Nullstellensatz we study the complexity of univariate ideal membership: Given \(f\in {\mathbb {F}}[X]\) by a circuit and polynomials

Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to arrive at linear Arrow-Debreu market equilibria. Jain (SIAM J. Comput. 37(1), 303–318, 2007) reduced equilibrium computation in linear Arrow-Debreu markets to the equilibrium computation

The Unsplittable Flow Cover problem (UFP-cover) models the well-studied general caching problem and various natural resource allocation settings. We are given a path with a demand on each edge and a set of tasks, each task being defined by a subpath and a size. The goal is to select a subset of the tasks of minimum cardinality such that on each edge e the total size of the selected tasks using e is

This paper is devoted to a new paradigm for the invariant recognition of visual objects through introducing ‘the generating invariant’ of the underlying visual geometry which allows to numerically calculate differential signature curves in a fully group-invariant manner. Then, we utilize the results to work on the unsolved problem of approximating similarity differential invariant signatures based

We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degree k, has size at most x. Collapsed k-Core was introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior

We study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and

We present algorithms for testing if a (0,1)-matrix M has Boolean/binary rank at most d, or is 𝜖-far from having Boolean/binary rank at most d (i.e., at least an 𝜖-fraction of the entries in M must be modified so that it has rank at most d). For the Boolean rank we present a non-adaptive testing algorithm whose query complexity is \(\tilde {O}\left (d^{4}/ \epsilon ^{6}\right )\). For the binary

We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is bn = n!. Our main result is that the sequence

Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic queries when the number of triangles on any edge in the graph is polylogarithmically bounded. Our query oracle Tripartite Independent Set (TIS) takes three disjoint

Restarting is a technique frequently employed in randomized algorithms. After some number of computation steps, the state of the algorithm is reinitialized with a new, independent random seed. Luby et al. (Inf. Process. Lett. 47(4), 173–180, 1993) introduced a universal restart strategy. They showed that their strategy is an optimal universal strategy in the worst case. However, the optimality result

In this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue

We study online scheduling of unit-sized jobs in two related problems, namely, restricted assignment problem and smart grid problem. The input to the two problems are in close analogy but the objective functions are different. We show that the greedy algorithm is an optimal online algorithm for both problems. Typically, an online algorithm is proved to be an optimal online algorithm through bounding

We study the growth rate of some power-free languages. For any integer k and real β > 1, we let α(k,β) be the growth rate of the number of β-free words of a given length over the alphabet {1,2,…,k}. Shur studied the asymptotic behavior of α(k,β) for β ≥ 2 as k goes to infinity. He suggested a conjecture regarding the asymptotic behavior of α(k,β) as k goes to infinity when 1 < β < 2. He showed that

We investigate the efficiency of fair allocations of indivisible goods using the well-studied price of fairness concept. Previous work has focused on classical fairness notions such as envy-freeness, proportionality, and equitability. However, these notions cannot always be satisfied for indivisible goods, leading to certain instances being ignored in the analysis. In this paper, we focus instead on

This work analyzes the minimum tollbooth problem in atomic network congestion games with unsplittable flows. The goal is to place tolls on edges, such that there exists a pure Nash equilibrium in the tolled game that is a social optimum in the untolled one. Additionally, we require the number of tolled edges to be the minimum. This problem has been extensively studied in non-atomic games, however,

In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply

We show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata. A max-plus tree automaton is called unambiguous if there is at most one accepting run on every tree. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton

Stateless ordered restart-delete automata (stl-ORD-automata) are studied. These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter. While the stl-ORWW-automata accept the regular languages, we show that the swift stl-ORD-automata yield a characterization

In the k-Connectivity Augmentation Problem we are given a k-edge-connected graph and a set of additional edges called links. Our goal is to find a set of links of minimum size whose addition to the graph makes it (k + 1)-edge-connected. There is an approximation preserving reduction from the mentioned problem to the case k = 1 (a.k.a. the Tree Augmentation Problem or TAP) or k = 2 (a.k.a. the Cactus

We discuss a game theoretic variant of the subset sum problem, in which two players compete for a common resource represented by a knapsack. Each player owns a private set of items, players pack items alternately, and each player either wants to maximize the total weight of his own items packed into the knapsack or to minimize the total weight of the items of the other player. We show that finding

Affine equivalent classes of Boolean functions have many applications in modern cryptography and circuit design. Previous publications have shown that affine equivalence on the entire space of Boolean functions can be computed up to 10 variables, but not on the quotient Boolean function space modulo functions of different degrees. Computing the number of equivalent classes of cosets of Reed-Muller

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