We study a security game over a network played between a defender and k attackers. Every attacker chooses, probabilistically, a node of the network to damage. The defender chooses, probabilistically as well, a connected induced subgraph of the network of \(\lambda \) nodes to scan and clean. Each attacker wishes to maximize the probability of escaping her cleaning by the defender. On the other hand

We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering \({\text{Top-}}{k}\) queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an \(m \times n\) array, with \(m \le n\), we first propose an encoding for answering 1-sided \({\textsf {Top}}{\text {-}}k{}\)

We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with fixed, complementary probabilities. Node addition follows the usual uniform attachment model. For node removal, we identify a class of deletion rules guaranteeing the current tree conditioned on its size is uniformly distributed over its range. By using generating function

We consider the complexity of recognizing k-clique-extendible graphs (k-C-E graphs) introduced by Spinrad (Efficient Graph Representations, AMS 2003), which are generalizations of comparability graphs. A graph is k-clique-extendible if there is an ordering of the vertices such that whenever two overlapping k-cliques A and B have \(k-1\) common vertices, and these common vertices appear between the

Given a metric space (X, d), a set of terminals \(K\subseteq X\), and a parameter \(0<\epsilon <1\), we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs in \(K\times X\) up to a factor of \(1+\epsilon\), and have small size (e.g. number of edges for spanners, dimension for embeddings). While such terminal (aka source-wise)

Biró et al. (Discrete. Math 100(1–3):267–279, 1992) introduced the concept of H-graphs, intersection graphs of connected subgraphs of a subdivision of a graph H. They are related to and generalize many important classes of geometric intersection graphs, e.g., interval graphs, circular-arc graphs, split graphs, and chordal graphs. Our paper starts a new line of research in the area of geometric intersection

The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a family of success-based updated rules that are determined by an update strength F and a success rate. We analyze in this work how the performance of the

The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs. Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A

We study the Online Budgeted Maximum Coverage problem. Subsets of a weighted ground set U arrive one by one, where each set has a cost. The online algorithm has to select a collection of sets, under the constraint that their cost is at most a given budget. Upon arrival of a set the algorithm must decide whether to accept or to irrevocably reject the arriving set, and it may also irrevocably drop previously

In the Token Jumping problem we are given a graph \(G = (V,E)\) and two independent sets S and T of G, each of size \(k \ge 1\). The goal is to determine whether there exists a sequence of k-sized independent sets in G, \(\langle S_0, S_1, \ldots , S_\ell \rangle\), such that for every i, \(|S_i| = k\), \(S_i\) is an independent set, \(S = S_0\), \(S_\ell = T\), and \(|S_i \varDelta S_{i+1}| = 2\)

Cyber security is a critical modern concern. Network intrusion detection systems (NIDS) perform protocol analysis, content searching and content matching, in order to detect harmful software. The high performance demands of NIDS applications in both speed and space consumption, as well as the diverse characteristics of the scenario conditions, have motivated a recent line of research on several formal

We study the multidimensional vector packing problem with selfish items. An item is a d-dimensional non-zero vector, whose rational components are in [0, 1]. A set of items can be packed into a bin if for every \(1 \le i \le d\), the sum of the ith components of all items of this set does not exceed 1. Items share costs of bins proportionally to the \(\ell _1\)-norms of items, and each item corresponds

Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic) random order ratio as an alternative performance measure for online algorithms. Here, an adversary specifies the items, but the order of arrival is drawn uniformly

In online edge- and node-deletion problems the input arrives node by node and an algorithm has to delete nodes or edges in order to keep the input graph in a given graph class \(\Pi \) at all times. We consider only hereditary properties \(\Pi \), for which optimal online algorithms exist and which can be characterized by a set of forbidden subgraphs \({{\mathcal{F}}}\) and analyze the advice complexity

We use queueing networks to present a new approach to solving Laplacian systems. This marks a significant departure from the existing techniques, mostly based on graph-theoretic constructions and sampling. Our distributed solver works for a large and important class of Laplacian systems that we call “one-sink” Laplacian systems. Specifically, our solver can produce solutions for systems of the form

We study the problem of truthfully scheduling m tasks to n selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen (in: The 31st Annual ACM symposium on Theory of Computing (STOC), 1999). Closing the current gap of [2.618, n] on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field

Quasiperiodicity in strings was introduced almost 30 years ago as an extension of string periodicity. The basic notions of quasiperiodicity are cover and seed. A cover of a text T is a string whose occurrences in T cover all positions of T. A seed of text T is a cover of a superstring of T. In various applications exact quasiperiodicity is still not sufficient due to the presence of errors. We consider

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting

Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to m identical parallel machines so as to minimize the maximum completion time of any job. Already in the 1960s, Graham showed that Greedy is \((2-1/m)\)-competitive. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201. No deterministic

For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a region homeomorphic to a closed disk such that (1) the subgraph induced by each cluster is drawn in the interior of the corresponding disk, (2) each edge intersects

Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is time-respecting, or temporal, if it uses edges with non-decreasing time stamps. We investigate a basic constraint

We introduce and investigate the approximability of the maximum binary tree problem (MBT) in directed and undirected graphs. The goal in MBT is to find a maximum-sized binary tree in a given graph. MBT is a natural variant of the well-studied longest path problem, since both can be viewed as finding a maximum-sized tree of bounded degree in a given graph. The connection to longest path motivates the

We study the complexity of the problems of finding, given a graph G, a largest induced subgraph of G with all degrees odd (called an odd subgraph), and the smallest number of odd subgraphs that partition V(G). We call these parameters \(\mathsf{mos}(G)\) and \(\chi _{\mathsf{odd}}(G)\), respectively. We prove that deciding whether \(\chi _{\mathsf{odd}}(G) \le q\) is polynomial-time solvable if \(q

Numerous combinatorial optimization problems (knapsack, maximum-weight matching, etc.) can be expressed as subset maximization problems: One is given a ground set \(N=\{1,\dots ,n\}\), a collection \(\mathcal {F}\subseteq 2^N\) of subsets thereof such that \(\emptyset \in \mathcal {F}\), and an objective (profit) function \(p:\mathcal {F}\rightarrow \mathbb {R}_+\). The task is to choose a set \(S\in

Mader conjectured in 2010 that for any tree T of order m, every k-connected graph G with minimum degree at least \(\lfloor \frac{3k}{2} \rfloor +m-1\) contains a subtree \(T' \cong T\) such that \(G-V(T')\) is k-connected. This conjecture has been proved for \(k = 1\); however, it remains open for general \(k \ge 2\); for \(k = 2\), partially affirmative answers have been shown, all of which restrict

The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search space can be discretized and represented by a binary tree, which can be explored by a Branch-and-Prune (BP) algorithm. It turns out that this combinatorial search

In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability notions, strongly stable noncrossing matching (SSNM) and weakly stable noncrossing matching (WSNM), depending on the strength of blocking pairs. They proved that a

Naor M., Parter M., Yogev E.: (The power of distributed verifiers in interactive proofs. In: 31st ACM-SIAM symposium on discrete algorithms (SODA), pp 1096–115, 2020. https://doi.org/10.1137/1.9781611975994.67) have recently demonstrated the existence of a distributed interactive proof for planarity (i.e., for certifying that a network is planar), using a sophisticated generic technique for constructing

Scaffolding is the final step in assembling Next Generation Sequencing data, in which pre-assembled contiguous regions (”contigs”) are oriented and ordered using information that links them (for example, mapping of paired-end reads). As the genome of some species is highly repetitive, we allow placing some contigs multiple times, thereby generalizing established computational models for this problem

Durand de Gevigney and Szigeti (J Gr Theory 91(4):305–325, 2019) have recently given a min–max theorem for the (2, k)-connectivity augmentation problem. This article provides an \(O(n^3(m+ n \text { }\log \text { }n))\) time algorithm to find an optimal solution for this problem.

We study the complexity of the two dual covering and packing distance-based problems Broadcast Domination and Multipacking in digraphs. A dominating broadcast of a digraph D is a function \(f:V(D)\rightarrow {\mathbb {N}}\) such that for each vertex v of D, there exists a vertex t with \(f(t)>0\) having a directed path to v of length at most f(t). The cost of f is the sum of f(v) over all vertices

We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary \(\mathsf {D}\) in fragments of a given string T of length n. The dictionary is internal in the sense that each pattern in \(\mathsf {D}\) is given as a fragment of T. This way, \(\mathsf {D}\) takes space proportional to the number of patterns \(d=|\mathsf {D}|\) rather than their total length

We study algorithmic properties of the graph class \({\textsc {Chordal}}{-ke}\), that is, graphs that can be turned into a chordal graph by adding at most k edges or, equivalently, the class of graphs of fill-in at most k. It appears that a number of fundamental intractable optimization problems being parameterized by k admit subexponential algorithms on graphs from \({\textsc {Chordal}}{-ke}\). More

Let P be a set of n colored points in the d-dimensional Euclidean space. Introduced by Hart (1968), a consistent subset of P, is a set \(S\subseteq P\) such that for every point p in \(P {\setminus } S\), the closest point of p in S has the same color as p. The consistent subset problem is to find a consistent subset of P with minimum cardinality. This problem is known to be NP-complete even for two-colored

We develop new approximation algorithms for classical graph and set problems in the RAM model under space constraints. As one of our main results, we devise an algorithm for \(d\text {-}\textsc {Hitting Set}{}\) that runs in time \(n^{{{\,\mathrm{O}\,}}{(d^2 + (d / \epsilon ))}}\), uses \({{\,\mathrm{O}\,}}{((d^2 + (d / \epsilon ))\log {n})}\) bits of space, and achieves an approximation ratio of \({{\

In this paper, we study the convex-straight-skeleton Voronoi diagrams of line segments and convex polygons. We explore the combinatorial complexity of these diagrams, and provide efficient algorithms for computing compact representations of them.

We consider the following control problem on fair allocation of indivisible goods. Given a set I of items and a set of agents, each having strict linear preferences over the items, we ask for a minimum subset of the items whose deletion guarantees the existence of a proportional allocation in the remaining instance; we call this problem Proportionality by Item Deletion (PID). Our main result is a polynomial-time

A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices is the same as their distance in the original graph. The Distance-Hereditary Vertex Deletion problem asks, given a graph G on n vertices and an integer k, whether there is a set S of at most k vertices in G such that \(G-S\) is distance-hereditary. This problem is

The problem of parameterized range majority asks us to preprocess a string of length n such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative frequencies in that range are more than a threshold \(\tau\). This is a more tractable version of the classical problem of finding the range mode, which is unlikely to be solvable in polylogarithmic time and linear

The rooted triplet distance measures the structural dissimilarity of two phylogenetic trees or phylogenetic networks by counting the number of rooted phylogenetic trees with exactly three leaf labels (called rooted triplets, or triplets for short) that occur as embedded subtrees in one, but not both, of them. Suppose that \(N_1 = (V_1, E_1)\) and \(N_2 = (V_2, E_2)\) are phylogenetic networks over

We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of lower bounds for the classic online bin packing problem. We apply a new method for weight based analysis, which is usually applied only in proofs of upper bounds

Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency of a highest-degree branching algorithm with a degree-based pruning. In this paper, we prove that this empirically fast algorithm runs in \(O(3.460^k n)\) time, where k is the solution size. This improves the previous best \(O(3.619^k n)\)-time deterministic algorithm obtained by Kociumaka and

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as k-center, k-median, and k-means. Such algorithms need to be both time and and space efficient. In this paper, we address the problem of correlation clustering in the dynamic data stream model. The stream consists of updates

In the Cluster Deletion problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of Cluster Deletion is NP-complete on (\(P_5\)-free) chordal graphs, whereas Cluster Deletion is solved in polynomial time on split graphs. However, the existence of a polynomial-time

We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem

A permutation is happy, if it can be transformed into the identity permutation using as many short swaps as one third times the number of inversions in the permutation. The complexity of the decision version of sorting a permutation by short swaps, is still open. We present an O(n) time algorithm to decide whether it is true for a permutation to be happy, where n is the number of elements in the permutation

For any fixed graph G, the subgraph isomorphism problem asks whether an n-vertex input graph has a subgraph isomorphic to G. A well-known algorithm of Alon et al. (J ACM 42(4):844–856, 1995. https://doi.org/10.1145/210332.210337) efficiently reduces this to the “colored” version of the problem, denoted \(G{\text{-}}{\mathsf {SUB}}\), and then solves \(G{\text{-}}{\mathsf {SUB}}\) in time \(O(n^{{\

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k. In this work we give two new algorithms for this well-studied problem

We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance \(\delta\) from each other. We investigate the complexity of this problem in terms of the rational parameter

A resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer. This problem is NP-complete, and remains so in very restricted classes of graphs. It is also W[2]-complete with respect to

Given a k-node pattern graph H and an n-node host graph G, the subgraph counting problem asks to compute the number of copies of H in G. In this work we address the following question: can we count the copies of H faster if G is sparse? We answer in the affirmative by introducing a novel tree-like decomposition for directed acyclic graphs, inspired by the classic tree decomposition for undirected graphs

A matching cut is a partition of the vertex set of a graph into two sets A and B such that each vertex has at most one neighbor in the other side of the cut. The Matching Cut problem asks whether a graph has a matching cut, and has been intensively studied in the literature. Motivated by a question posed by Komusiewicz et al. [Discrete Applied Mathematics, 2020], we introduce a natural generalization

The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival

A bicolored rectangular family BRF is the collection of all axis-parallel rectangles formed by selecting a bottom-left corner from a finite set of points A and an upper-right corner from a finite set of points B. We devise a combinatorial algorithm to compute the maximum independent set and the minimum hitting set of a BRF that runs in \(O(n^{2.5}\sqrt{\log n})\)-time, where \(n=|A |+|B |\). This result

This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given k weighted-matroids on the same ground set. Our goal is to find a feasible partition that minimizes (maximizes) the value of an objective function. A typical objective is the maximum over all subsets of the total weights of the elements in a subset, which is extensively studied in

We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi-start (\(\mu\)+1) GA solves arbitrary length-n instances of closest string in \(2^{O(d^2 + d \log k)} \cdot t(n)\) steps in expectation. Here, k is the number of strings in the input

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths of a certain length. It has been shown that transportation networks, on which TSP and STP naturally occur for various applications in logistics, typically have a small highway dimension. While

Given an n-vertex digraph D and a non-negative integer k, the Minimum Directed Bisection problem asks if the vertices of D can be partitioned into two parts, say L and R, such that \({\vert {L} \vert }\) and \({\vert {R} \vert }\) differ by at most 1 and the number of arcs from R to L is at most k. This problem is known to be NP-hard even when \(k = 0\). We investigate the parameterized complexity

In the eternal domination game played on graphs, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices on their turn. The goal is to determine the eternal domination number \(\gamma ^{\infty }_{all}\) of a graph, which is the minimum number of guards required to defend against an infinite sequence