# Algorithmica

## List of Papers (Total 199)

#### Optimal Online Two-Way Trading with Bounded Number of Transactions

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...

#### Level-Based Analysis of the Univariate Marginal Distribution Algorithm

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...

#### Dynamic Graph Stream Algorithms in o(n) Space

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...

#### Backdoors for Linear Temporal Logic

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...

#### Computing the Number of Induced Copies of a Fixed Graph in a Bounded Degree Graph

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...

#### On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

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...

#### Extreme Witnesses and Their Applications

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...

#### Tight Conditional Lower Bounds for Longest Common Increasing Subsequence

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...

#### Independent Feedback Vertex Set for $$P_5$$ -Free Graphs

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...

#### Approximation Schemes for Minimizing the Maximum Lateness on a Single Machine with Release Times Under Non-availability or Deadline Constraints

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...