The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer \(k\ge 0\), to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an...

The problem of pollution control has been mainly studied in the environmental economics literature where the methodology of game theory is applied for the pollution control. To the best of our knowledge this is the first time this problem is studied from the computational point of view. We introduce a new network model for pollution control and present two applications of this...

We study storyboarding where advertisers wish to present sequences of ads (stories) uninterruptedly on a major ad position of a web page. These jobs/stories arrive online and are triggered by the browsing history of a user who at any time continues surfing with probability \(\beta \). The goal of an ad server is to construct a schedule maximizing the expected reward. The problem...

In this paper, we consider four single-machine scheduling problems with release times, with the aim of minimizing the maximum lateness. In the first problem we have a common deadline for all the jobs. The second problem looks for the Pareto frontier with respect to the two objective functions maximum lateness and makespan. The third problem is associated with a non-availability...

Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this...

The classical paging problem is to maintain a two-level memory system so that a sequence of requests to memory pages can be served with a small number of faults. Standard competitive analysis gives overly pessimistic results as it ignores the fact that real-world input sequences exhibit locality of reference. Initiated by a paper of Borodin et al. (J Comput Syst Sci 50:244–258...

Many combinatorial problems involve determining whether a universe of n elements contains a witness consisting of k elements which have some specified property. In this paper we investigate the relationship between the decision and enumeration versions of such problems: efficient methods are known for transforming a decision algorithm into a search procedure that finds a single...

We give a kernel with \(O(k^7)\) vertices for Trivially Perfect Editing, the problem of adding or removing at most k edges in order to make a given graph trivially perfect. This answers in affirmative an open question posed by Nastos and Gao (Soc Netw 35(3):439–450, 2013), and by Liu et al. (Tsinghua Sci Technol 19(4):346–357, 2014). Our general technique implies also the...

We study the following problem: preprocess a set \(\mathcal {O}\) of objects into a data structure that allows us to efficiently report all pairs of objects from \(\mathcal {O}\) that intersect inside an axis-aligned query range \({Q}\). We present data structures of size \(O(n\cdot {{\mathrm{polylog\,}}}n)\) and with query time \(O((k+1)\cdot {{\mathrm{polylog\,}}}n)\) time...

The maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several...

In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is \(W[1]\)-hard...

The authors regret the following error in their article “A connection between sports and matroids: How many teams can we beat?” (Algorithmica, doi: 10.1007/s00453-016-0256-2), considering the computational complexity of the problem MinStanding(S). In Theorem 3 of our paper [4], we erroneously claimed a \(\mathsf {W}[1]\)-hardness result to hold even for the case where the...

Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to \(\lambda \) islands optimizing the so-called Maze fitness function (K...

We consider two-player zero-sum stochastic mean payoff games with perfect information. We show that any such game, with a constant number of random positions and polynomially bounded positive transition probabilities, admits a polynomial time approximation scheme, both in the relative and absolute sense.

Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in...

The hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view accurately inferring the root location in a phylogenetic tree is notoriously difficult and poor root placement can artificially inflate the...