Related papers: A $\frac{3}{2}$-Approximation Algorithm for Tree A…
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied…
The capacitated tree cover problem with edge loads is a variant of the tree cover problem, where we are given facility opening costs, edge costs and loads, as well as vertex loads. We try to find a tree cover of minimum cost such that the…
We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…
We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show…
In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is…
Our motivation is to improve on the best approximation guarantee known for the problem of finding a minimum-cost 2-node connected spanning subgraph of a given undirected graph with nonnegative edge costs. We present an LP (Linear…
We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning…
Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…
The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation…
Given a connected undirected graph $\bar{G}$ on $n$ vertices, and non-negative edge costs $c$, the 2ECM problem is that of finding a $2$-edge~connected spanning multisubgraph of $\bar{G}$ of minimum cost. The natural linear program (LP) for…
We present a $\frac74$ approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
We design and analyse approximation algorithms for the minimum-cost connected T-join problem: given an undirected graph G = (V;E) with nonnegative costs on the edges, and a subset of nodes T, find (if it exists) a spanning connected…
We study the online multi-level aggregation problem with deadlines (MLAP-D) introduced by Bienkowski et al. (ESA 2016, OR 2020). In this problem, requests arrive over time at the vertices of a given vertex-weighted tree, and each request…
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and M\"uhlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), and IPCO 2020:…
The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings.…
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum…