Algorithmica

List of Papers (Total 185)

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...

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...

Network Pollution Games

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...

New Online Algorithms for Story Scheduling in Web Advertising

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...

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...

An Improved Approximation Algorithm for Knapsack Median Using Sparsification

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...

Quantifying Competitiveness in Paging with Locality of Reference

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...

Randomised Enumeration of Small Witnesses Using a Decision Oracle

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...

A Polynomial Kernel for Trivially Perfect Editing

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...

Finding Pairwise Intersections Inside a Query Range

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...

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

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...

Complexity of Token Swapping and Its Variants

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...

Correction to: A Connection Between Sports and Matroids: How Many Teams Can We Beat?

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...

The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization

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...

Approximation Schemes for Stochastic Mean Payoff Games with Perfect Information and Few Random Positions

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.