We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to k trades, where each trade must involve the full amount. We give optimal algorithms for three different models which differ in the knowledge of how the price fluctuates. In the first model...

Estimation of Distribution Algorithms (EDAs) are stochastic heuristics that search for optimal solutions by learning and sampling from probabilistic models. Despite their popularity in real-world applications, there is little rigorous understanding of their performance. Even for the Univariate Marginal Distribution Algorithm (UMDA)—a simple population-based EDA assuming...

In this paper we study graph problems in the dynamic streaming model, where the input is defined by a sequence of edge insertions and deletions. As many natural problems require \(\varOmega (n)\) space, where n is the number of vertices, existing works mainly focused on designing \({O}(n\cdot \mathrm {poly}\log n)\) space algorithms. Although sublinear in the number of edges for...

In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we...

In this paper we show that for any graph H of order m and any graph G of order n and maximum degree \(\Delta \) one can compute the number of subsets S of V(G) that induces a graph isomorphic to H in time \(O(c^m \cdot n )\) for some constant \(c = c(\Delta ) >0\). This is essentially best possible (in the sense that there is no \(c^{o(m)}poly(n)\)-time algorithm under the...

In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and an integer \(r>1\), and the goal is to design an approximation algorithm with the fastest possible running time. We give randomized algorithms that establish an approximation ratio of1. r for maximum independent set in \(O^*(\exp ({\tilde{O...

Given an edge-weighted graph G with a set \(Q\) of k terminals, a mimicking network is a graph with the same set of terminals that exactly preserves the size of minimum cut between any partition of the terminals. A natural question in the area of graph compression is to provide as small mimicking networks as possible for input graph G being either an arbitrary graph or coming...

Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns...

We study the problem of computing the so called minimum and maximum witnesses for Boolean vector convolution. We also consider a generalization of the problem which is to determine for each positive value at a coordinate of the convolution vector, q smallest (largest) witnesses, where q is the minimum of a parameter k and the number of witnesses for this coordinate. We term this...

We consider the canonical generalization of the well-studied Longest Increasing Subsequence problem to multiple sequences, called k-LCIS: Given k integer sequences \(X_1,\dots ,X_k\) of length at most n, the task is to determine the length of the longest common subsequence of \(X_1,\dots ,X_k\) that is also strictly increasing. Especially for the case of \(k=2\) (called LCIS for...

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...

In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any \(d>0\), the first algorithm maintains a proper \(O...

We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the two players’ payoffs), our algorithm first solves two independent LPs, each of which is derived from one of the two payoff matrices, and then...

Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot...

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...