Related papers: Approximating Upper Degree-Constrained Partial Ori…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
We study the partial search order problem (PSOP) proposed recently by Scheffler [WG 2022]. Given a graph $G$ together with a partial order over the set of vertices of $G$, this problem determines if there is an $\mathcal{S}$-ordering that…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
The orientation completion problem for a class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class by orienting the unoriented edges of the partially oriented graph.…
A monitoring edge-geodetic set of a graph is a subset $M$ of its vertices such that for every edge $e$ in the graph, deleting $e$ increases the distance between at least one pair of vertices in $M$. We study the following computational…