相关论文: Breaching the 2-Approximation Barrier for Connecti…

This note concerns the trade-off between the degree of the constraint graph and the gap in hardness of approximating the Min-Rep variant of Label Cover (aka Projection Game). We make a very simple observation that, for NP-hardness with gap…

Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…

Finding a Steiner strongly $k$-arc-connected orientation is particularly relevant in network design and reliability, as it guarantees robust communication between a designated set of critical nodes. Kir\'aly and Lau (FOCS 2006) introduced a…

Link prediction is a crucial task in many downstream applications of graph machine learning. To this end, Graph Neural Network (GNN) is a widely used technique for link prediction, mainly in transductive settings, where the goal is to…

The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…

We give improved approximations for two metric Traveling Salesman Problem (TSP) variants. In Ordered TSP (OTSP) we are given a linear ordering on a subset of nodes $o_1, \ldots, o_k$. The TSP solution must have that $o_{i+1}$ is visited at…

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 a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…

Markov Networks are widely used through out computer vision and machine learning. An important subclass are the Associative Markov Networks which are used in a wide variety of applications. For these networks a good approximate minimum cost…

The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization…

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover…

We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian…

In two-stage robust optimization the solution to a problem is built in two stages: In the first stage a partial, not necessarily feasible, solution is exhibited. Then the adversary chooses the "worst" scenario from a predefined set of…

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 Hop-Constrained Steiner Tree problem (HCST) is challenging NP-hard problem arising in the design of centralized telecommunication networks where the reliability constraints matter. In this paper three iterative greedy algorithms are…

In this paper, we study a survivable network design problem on directed graphs, 2-Connected Directed Steiner Tree (2-DST): given an $n$-vertex weighted directed graph, a root $r$, and a set of $h$ terminals $S$, find a min-cost subgraph $H$…

In the 2-Vertex-Connected Spanning Subgraph problem (2-VCSS), we are given an undirected graph $G$, and the objective is to find a 2-vertex-connected spanning subgraph $S$ of $G$ with the minimum number of edges. In the context of…

We initiate the theoretical study of the problem of minimizing the size of an iBGP overlay in an Autonomous System (AS) in the Internet subject to a natural notion of correctness derived from the standard "hot-potato" routing rules. For…

Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…

Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…