We introduce a framework for sparsity structures defined via graphs. Our approach is flexible
and generalizes several previously studied sparsity models. Moreover, we provide efficient …

We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest
problem on planar graphs and, more generally, on graphs of bounded genus. As a first step …

Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop
vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is …

We present a new approximation algorithm for the (metric) prize-collecting traveling
salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson …

Abstract The Maximum (Node-) Weight Connected Subgraph Problem (MWCS) searches for
a connected subgraph with maximum total weight in a node-weighted (di) graph. In this work …

We prove that any graph excluding a fixed minor can have its edges partitioned into a
desired number k of color classes such that contracting the edges in any one color class …

Graphs with bounded highway dimension were introduced by Abraham et al. Proceedings of
SODA 2010, pp. 782--793 as a model of transportation networks. We show that any such …

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V
to optimality in O (Btw+ 22⋅ tw⋅| V|) time, where tw is the graphʼs treewidth and the Bell …

We present the first polynomial-time approximation schemes (PTAS es) for the following
subset-connectivity problems in edge-weighted graphs of bounded-genus: Steiner tree, low …

In this paper, we reduce Prize-Collecting Steiner TSP (PCTSP), Prize-Collecting Stroll
(PCS), Prize-Collecting Steiner Tree (PCST), Prize-Collecting Steiner Forest (PCSF), and …