Related papers: FPT algorithms over linear delta-matroids with app…
The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where…
In the Maximize Phylogenetic Diversity problem, we are given a phylogenetic tree that represents the genetic proximity of species, and we are asked to select a subset of species of maximum phylogenetic diversity to be preserved through…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…
In this work, we study the $d$-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of $r$ solutions of size at most $k$ each, which has recently been introduced to the field of parameterized…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Matroid intersection is one of the most powerful frameworks of matroid theory that generalizes various problems in combinatorial optimization. Edmonds' fundamental theorem provides a min-max characterization for the unweighted setting,…
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving…
In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms.…
While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of $2$ for the \emph{unweighted} matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted…
The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…
The investigation of width parameters in both graph and algebraic contexts has attracted considerable interest. Among these parameters, the linear branch width has emerged as a crucial measure. In this concise paper, we explore the concept…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…
We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and…
In this paper, we address the weighted linear matroid intersection problem from the computation of the degree of the determinants of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants,…
A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…