Related papers: Parameterized Approximation Algorithms for Packing…
We show how to restrict the analysis of a class of online problems that includes the $k$-server problem in finite metrics such that we only have to consider finite sequences of request. When applying the restrictions, both the optimal…
Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
Sampling-based motion planning algorithms have been continuously developed for more than two decades. Apart from mobile robots, they are also widely used in manipulator motion planning. Hence, these methods play a key role in collaborative…
The $k$-Median problem is one of the well-known optimization problems that formalize the task of data clustering. Here, we are given sets of facilities $F$ and clients $C$, and the goal is to open $k$ facilities from the set $F$, which…
We discuss guidelines for evaluating the performance of parameterized stochastic solvers for optimization problems, with particular attention to systems that employ novel hardware, such as digital quantum processors running variational…
Computing all-pairs shortest paths is a fundamental and much-studied problem with many applications. Unfortunately, despite intense study, there are still no significantly faster algorithms for it than the $\mathcal{O}(n^3)$ time algorithm…
Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of…
Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some…
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a…
The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into…
In the $k$-cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. The current best algorithms are an…