Related papers: The two-edge connectivity survivable-network desig…
We consider the problem of finding the minimum-weight subgraph that satisfies given connectivity requirements. Specifically, given a requirement $r \in \{0,1,2,3\}$ for every vertex, we seek the minimum-weight subgraph that contains, for…
The geometric bottleneck Steiner network problem on a set of vertices $X$ embedded in a normed plane requires one to construct a graph $G$ spanning $X$ and a variable set of $k\geq 0$ additional points, such that the length of the longest…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
We consider node-weighted survivable network design (SNDP) in planar graphs and minor-closed families of graphs. The input consists of a node-weighted undirected graph $G=(V,E)$ and integer connectivity requirements $r(uv)$ for each…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2…
In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph…
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The…
Given $k$ pairs of terminals $\{(s_{1}, t_{1}), \ldots, (s_{k}, t_{k})\}$ in a graph $G$, the min-sum $k$ vertex-disjoint paths problem is to find a collection $\{Q_{1}, Q_{2}, \ldots, Q_{k}\}$ of vertex-disjoint paths with minimum total…
We study the following Two-Sets Cut-Uncut problem on planar graphs. Therein, one is given an undirected planar graph $G$ and two sets of vertices $S$ and $T$. The question is, what is the minimum number of edges to remove from $G$, such…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the…
We consider dynamic subgraph connectivity problems for planar graphs. In this model there is a fixed underlying planar graph, where each edge and vertex is either "off" (failed) or "on" (recovered). We wish to answer connectivity queries…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
The complexity of the maximum common connected subgraph problem in partial $k$-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial $2$-trees. On the other…
For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph $G$ with edge costs, a set $R$ of terminal vertices, and an integer demand $d_{s,t}$ for every terminal pair $s,t\in R$. The task is to compute a…
Bottleneck Steiner networks model energy consumption in wireless ad-hoc networks. The task is to design a network spanning a given set of terminals and at most $k$ Steiner points such that the length of the longest edge is minimised. The…
The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s_0,t_0), ...,(s_k,t_k), whether there are k+1 pairwise disjoint paths P_0, ...,P_k, such that P_i connects s_i to t_i. Robertson and Seymour have proven that…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the…