Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static graphs, which often stand in contrast to practice where data is inherently dynamic. A temporal graph has an edge set that changes over time. We present a natural temporal

Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List

For a graph invariant π, the Contraction(π) problem consists of, given a graph G and positive integers k,d, deciding whether one can contract k edges of G to obtain a graph in which π has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] studied the case where π is the size of a minimum dominating set. We focus on graph invariants defined as the minimum size of a vertex set that hits all

The parity argument principle states that every finite graph has an even number of odd degree vertices. We consider the problem whose totality is guaranteed by the parity argument on a graph with potential. In this paper, we show that the problem of finding an unknown odd-degree vertex or a local optimum vertex on a graph with potential is polynomially equivalent to EndOfPotentialLine if the maximum

An order-k univariate spline is a function defined over a set S of at least k+2 real parameters, called knots. Such a spline can be obtained as a linear combination of B-splines, each of them being defined over a subset of k+2 consecutive knots of S, called a configuration of S. In the bivariate setting, knots are pairs of reals and B-splines are defined over configurations of k+3 knots. Using convex

We consider a function-analytic approach to study synchronizing automata, primitive and ergodic matrix families. This gives a new way to establish some criteria for primitivity and for ergodicity of families of nonnegative matrices. We introduce a concept of canonical partition and use it to construct a polynomial-time algorithm for finding a positive matrix product and an ergodic matrix product whenever

This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. In particular, we study the complexity of finding values for these parameters such that the induced MDP satisfies some maximal or minimal

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium. But sometimes several equilibria may coexist. For instance we can have two equilibria: a first one where no player reaches his target set and an other one where all the players reach their target

The rankable and the compressible sets have been studied for more than a quarter of a century. We ask whether these classes are closed under the most important boolean and other operations. We study this question for both polynomial-time and recursion-theoretic compression and ranking, and for almost every case arrive at a Closed, a Not-Closed, or a Closed-Iff-Well-Known-Complexity-Classes-Collapse

For a fixed finite family of graphs F, the F-Minor-Free Deletion problem takes as input a graph G and integer ℓ and asks whether a size-ℓ vertex set X exists such that G−X is F-minor-free. {K2}-Minor-Free Deletion and {K3}-Minor-Free Deletion encode Vertex Cover and Feedback Vertex Set respectively. When parameterized by the feedback vertex number of G these two problems are known to admit a polynomial

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. We prove that the inflationary and partial fixed point variants of this logic capture PolylogTime and PolylogSpace

A graph game proceeds as follows: two players move a token through a graph to produce a finite or infinite path, which determines the payoff of the game. We study bidding games in which in each turn, an auction determines which player moves the token. Bidding games were largely studied in combination with two variants of first-price auctions called “Richman” and “poorman” bidding. We study taxman bidding

We prove that if (min⁡,+)-Convolution can be solved in O(τ(n)) time, then Bisection on treewidth t graphs can be solved in time O(8ttO(1)log⁡n⋅τ(n)), assuming a decomposition of width t as input. Plugging in the O(n2) time algorithm for (min⁡,+)-Convolution yields a O(8ttO(1)n2log⁡n) time algorithm for Bisection. This improves over the (dependence on n of the) O(2tn3) time algorithm of Jansen et al

We consider the feature-generation task wherein we are given a database with entities labeled as positive and negative examples, and we want to find feature queries that linearly separate the two sets of examples. We focus on conjunctive feature queries, and explore two problems: (a) deciding if separating feature queries exist (separability), and (b) generating such queries when they exist. To restrict

Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these processes spread are dynamic in nature, and can be modelled with temporal graphs. Here, we study the problem of deleting edges from a given temporal graph in order

The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is known that both problems are undecidable. We provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata. We show that a gap version of the emptiness problem (known

A channel with multiplicity feedback in case of collision returns the exact number of stations simultaneously transmitting. In this model, Θ((dlog⁡(n/d))/log⁡d) time rounds are sufficient and necessary to identify d transmitting stations out of n. In contrast, in the ternary feedback model the time complexity is Θ(dlog⁡(n/d)). Generalizing, we can define a feedback interval [x,y], where 0≤x≤y≤d, such

Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal syntax. We consider an extension of nominal syntax with non-capturing atom substitutions and show that

The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk that starts at a given start node, visits all nodes of the graph, and has the smallest arrival time. In the first and second part of the paper, we consider only undirected temporal graphs that are connected at each time step. For such temporal graphs with

In this paper, we study the Maximum Internal Spanning Tree Problem (MIST). Given an undirected simple graph G, the task for the Maximum Internal Spanning Tree problem is to find a spanning tree of G with maximum number of internal vertices. We present an approximation algorithm with performance ratio 43, which improves upon the best known performance ratio 32. Our algorithm benefits from a new observation

Henzinger et al. posed the so-called Online Boolean Matrix-vector Multiplication (OMv) conjecture and showed that it implies tight hardness results for several basic dynamic or partially dynamic problems [STOC'15]. We first show that the OMv conjecture is implied by a simple off-line conjecture that we call the MvP conjecture. We then show that if the definition of the OMv conjecture is generalized

The degree distribution of an ordered tree T with n nodes is n→=(n0,…,nn−1), where ni is the number of nodes in T with i children. Let N(n→) be the number of trees with degree distribution n→. We give a data structure that stores an ordered tree T with n nodes and degree distribution n→ using log⁡N(n→)+O(n/logt⁡n) bits for every constant t. The data structure answers tree queries in constant time.

In this paper we characterize normal sequences and finite-state dimension in terms of the automatic Kolmogorov complexity and finite-state a priori probability. We show that many known results about normal sequences and finite-state dimension, including the equivalence between aligned and non-aligned normality, Wall's theorem, Piatetski–Shapiro's theorem, Champernowne's example of normal number and

The expensive cost and intermittent availability of renewable energy bring great challenges to its efficient utilization in green data centers. In this paper, we propose a new way to achieve an explicit trade-off between operational cost and carbon emission by dynamic storing off-site renewable energy in distributed data centers. We first formulate a constrained stochastic optimization problem for

Let a text T[1..n] be the only string generated by a context-free grammar with g (terminal and nonterminal) symbols, and of size G (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a grammar-compressed representation of T, can be encoded using Glg⁡G bits. We introduce the first grammar-compressed index that uses O(Glg⁡n) bits (precisely, Glg⁡n+(2+ϵ)Glg⁡g

It is well known that hyperedge-replacement grammars can generate NP-complete graph languages even under seemingly harsh restrictions. This means that the parsing problem is difficult even in the non-uniform setting, in which the grammar is considered to be fixed rather than being part of the input. Little is known about restrictions under which truly uniform polynomial parsing is possible. In this

The modularity is the best known and widely used quality function for community detection in graphs. We investigate the approximability of the modularity maximization problem and some related problems. We first design a polynomial-time 0.4209-additive approximation algorithm for the modularity maximization problem, which improves the current best additive approximation error of 0.4672. Our theoretical

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we address this shortcoming by showing that the problem is fixed parameter tractable. We do this by establishing a linear kernel i.e., that after applying certain

Timed pushdown automata (tpda) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of tpda are expressible in linear arithmetic, a rich logic generalising Presburger arithmetic and rational arithmetic. The main technical ingredients are a novel quantifier elimination result for clock constraints (used to simplify the syntax of

We study the problem of counting the repairs of an inconsistent database in the case where constraints are Functional Dependencies (FDs). A repair is then a maximal independent set of the conflict graph, wherein nodes represent facts and edges represent violations. We establish a dichotomy in data complexity for the complete space of FDs: when the FD set has, up to equivalence, what we call a “left-hand-side

The main contributions of the paper are summarized as follows. We take an analytical approach in the sense that the quality of service and the price of service as well as the revenue, cost, and profit of a cloud service provider (CSP) can all be quantitatively available based on well established analytical models. We argue that the satisfaction of a customer includes two aspects, i.e., satisfaction

We study selective monitors for labelled Markov chains. Monitors observe the outputs that are generated by a Markov chain during its run, with the goal of identifying runs as correct or faulty. A monitor is selective if it skips observations in order to reduce monitoring overhead. We are interested in monitors that minimize the expected number of observations. We establish an undecidability result

In k-Clustering we are given a multiset of n vectors X⊂Zd and a nonnegative number D, and we need to decide whether X can be partitioned into k clusters C1,…,Ck such that the cost∑i=1kminci∈Rd⁡∑x∈Ci‖x−ci‖pp≤D, where ‖⋅‖p is the Lp-norm. For p=2, k-Clustering is k-Means. We study k-Clustering from the perspective of parameterized complexity. The problem is known to be NP-hard for k=2 and also for d=2

We study the problem of finding an exact solution to the Consensus Halving problem. While recent work has shown that the approximate version of this problem is PPA -complete [29], [30], we show that the exact version is much harder. Specifically, finding a solution with n agents and n cuts is FIXP -hard, and deciding whether there exists a solution with fewer than n cuts is ETR -complete. Along the

Let string S[1..n] be parsed into z phrases by the Lempel-Ziv algorithm. The corresponding compression algorithm encodes S in O(z) space, but it does not support random access to S. We introduce a data structure, the block tree, that represents S in O(zlog⁡(n/z)) space and extracts any symbol of S in time O(log⁡(n/z)), among other space-time tradeoffs. The structure also supports other queries that

The inverse satisfiability problem over a set of relations Γ (Inv-SAT(Γ)) is the problem of deciding whether a relation R can be defined as the set of models of a SAT(Γ) instance. Kavvadias and Sideri (1998) [15] obtained a dichotomy between P and co-NP-complete for finite Γ containing the two constant Boolean relations. However, for arbitrary constraint languages the complexity has been wide open

We consider weighted congestion games with polynomial latency functions of maximum degree d≥1. For these games, we investigate the existence and efficiency of approximate pure Nash equilibria which are obtained through sequences of unilateral improvement moves by the players. By exploiting a simple technique, we firstly show that these games admit an infinite set of d-approximate potential functions

In 2003, Fischlin introduced the concept of progressive verification in cryptography to relate the error probability of a cryptographic verification procedure to its running time. It ensures that the verifier confidence in the validity of a verification procedure grows with the work it invests in the computation. Le, Kelkar and Kate recently revisited this approach for digital signatures and proposed

In this paper, we introduce the model of quantum Mealy machines and study the equivalence checking and minimisation problems of them. Two efficient algorithms are developed for checking equivalence of two states in the same machine and for checking equivalence of two machines. As an application, they are used in equivalence checking of quantum circuits. Moreover, the minimisation problem is proved

A family of tree automata of size n is presented such that the size of the largest common prefix (lcp) tree of all accepted trees is exponential in n. Moreover, it is shown that this prefix tree is not compressible via DAGs (directed acyclic graphs) or tree straight-line programs. We also show that determining whether or not the lcp trees of two given tree automata are equal is coNP-complete; the result

We study two problems where k autonomous mobile agents are initially located on distinct nodes of a weighted graph with n nodes and m edges. Each agent has a predefined velocity and can only move along the edges of the graph. The first problem is to deliver one package from a source node to a destination node. The second is to simultaneously deliver two packages, each from its source node to its destination

We study the complexity of #CSPΔ(Γ), which is the problem of counting satisfying assignments to CSP instances with constraints from Γ and whose variables can appear at most Δ times. Our main result shows that: (i) if every function in Γ is affine, then #CSPΔ(Γ) is in FP for all Δ, (ii) otherwise, if every function in Γ is in a class called IM2, then for large Δ, #CSPΔ(Γ) is equivalent under approximation-preserving

Given a subset of states S of a deterministic finite automaton and a word w, the preimage is the subset of all states mapped to a state in S by the action of w. We study three natural problems concerning words giving certain preimages. The first problem is whether, for a given subset, there exists a word extending the subset (giving a larger preimage). The second problem is whether there exists a totally

Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g. the spread of disease or dissemination of information. Motivated by real-world applications, modification of static graphs to control this spread has proven a rich topic for previous research. Here, we introduce a new type of modification for temporal graphs: the number

This work studies multi-broadcasting for the SINR (Signal-to-Interference-plus-Noise-Ratio) model, assuming a subset of nodes are initially awake, when each device only has access to knowledge about the total number of nodes in the network n, the range from which each node's label is taken {1,…,N}, and the label of the device itself. We assume no knowledge of the physical coordinates of devices and

We show that computation of the SPERNER problem is PPA-complete on the Möbius band under proper boundary conditions, settling a long term open problem. Further, the same computational complexity results extend to other discrete fixed points on the Möbius band, such as the Brouwer fixed point problem, the DPZP fixed point problem and a simple version of the Tucker problem, as well as the projective

We consider a family of skew tent maps fa on the unit interval, determined by the parameter a, with 0

A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by Sénizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for deterministic pushdown automata. The presented proof is conceptually simpler, and a particular novelty is that it is not given as two semidecision procedures but it provides

We consider the circular pattern matching with k mismatches (k-CPM) problem in which one is to compute the minimal Hamming distance of every length-m substring of T and any cyclic rotation of P, if this distance is no more than k. It is a variation of the well-studied k-mismatch problem. A multitude of papers has been devoted to solving the k-CPM problem, but only average-case upper bounds are known

Edge fault-tolerance of interconnection network is of significant important to the design and maintenance of multiprocessor systems. A connected graph G is maximally edge-connected (maximally-λ for short) if its edge-connectivity attains its minimum degree. G is super edge-connected (super-λ for short) if every minimum edge-cut isolates one vertex. The edge fault-tolerance of the maximally-λ (resp

Let M=(T,C,P) be a security model, where T is a rooted tree, C is a multiset of costs and P is a multiset of prizes and let (T,c,p) be a security system, where c and p are bijections of costs and prizes. The problems of computing an optimal attack on a security system and of determining an edge e∈E(T) such that the maximum sum of prizes obtained from an optimal attack in (T,c,p) is minimized when c(e)=∞

In this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search strategy initially assigns labels to the searchers, each searcher can be only present on an edge of its own label. We prove that this problem is not monotone even for

Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport's happened-before relation. To this end, we introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results

The Cayley table representation of a group uses O(n2) words for a group of order n and answers multiplication queries in time O(1). It is interesting to ask if there is a o(n2) space representation of groups that still has O(1) query-time. We show that for any δ, 1/log⁡n≤δ≤1, there is an O(n1+δ/δ) space representation for groups of order n with O(1/δ) query-time. We also show that for Dedekind groups

We study the expressive power of 1-way data-independent finite automata with k heads (1DiDFA(k)). The data-independence means that the trajectory of each head during a computation depends only on the length of the input word. It has long been known that “k+1 heads are better than k” for the (data-dependent) 1DFA(k), and (2-way) 2DiDFA(k). However, somewhat surprisingly, no such hierarchy has been known

In public key encryption with keyword search (PEKS), a secure channel is required in order to send trapdoors to the server, whereas in secure-channel free PEKS (SCF-PEKS), no such secure channel is required. In this paper, we propose a generic construction of SCF-PEKS with multiple keywords (SCF-MPEKS) from hidden vector encryption, tag-based encryption, and a one-time signature. Our generic construction

Galled trees are studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into tree-child and galled network classes by relaxing a structural condition imposed on galled trees. We provide a solution to an open problem that is how to count and enumerate tree-child networks with fixed number of leaves and reticulations. Explicit counting formulas are

We study stability of routing in multi-hop wireless networks in the framework of adversarial queueing. A routing algorithm consists of three components: a transmission policy to decide on immediate transmissions, a scheduling policy to select a packet to transmit, and a hearing control to coordinate transmissions with scheduling. We consider two kinds of hearing control: proactive and reactive. We

The complexity class CLS was proposed by Daskalakis and Papadimitriou in 2011 to understand the complexity of important NP search problems that admit both path following and potential optimizing algorithms. Here we identify a subclass of CLS – called UniqueEOPL – that applies a more specific combinatorial principle that guarantees unique solutions. We show that UniqueEOPL contains several important

Temporal graphs abstractly model real-life inherently dynamic networks. Given a graph G, a temporal graph with G as the underlying graph is a sequence of subgraphs (snapshots) Gt of G, where t≥1. In this paper we study stochastic temporal graphs, i.e. stochastic processes G whose random variables are the snapshots of a temporal graph on G. A natural feature observed in various real-life scenarios is