Related papers: Lower Bounds on Flow Sparsifiers with Steiner Node…
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.…
Let $H$ be an edge-weighted graph, and let $G$ be a subgraph of $H$. We say that $G$ is an $f$-fault-tolerant $t$-spanner for $H$, if the following is true for any subset $F$ of at most $f$ edges of $G$: For any two vertices $p$ and $q$,…
We give an algorithm to route a multicommodity flow in a planar graph $G$ with congestion $O(\log k)$, where $k$ is the maximum number of terminals on the boundary of a face, when each demand edge lie on a face of $G$. We also show that our…
We present a compact labeling scheme for determining whether a designated set of terminals in a graph remains connected after any $f$ (or less) vertex failures occur. An $f$-FT Steiner connectivity labeling scheme for an $n$-vertex graph…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. Given a single pass over a stream containing insertions and deletions of edges to a graph G, our algorithm…
We study vertex cut and flow sparsifiers that were recently introduced by Moitra, and Leighton and Moitra. We improve and generalize their results. We give a new polynomial-time algorithm for constructing O(log k / log log k) cut and flow…
A cut sparsifier is a reweighted subgraph that maintains the weights of the cuts of the original graph up to a multiplicative factor of $(1\pm\epsilon)$. This paper considers computing cut sparsifiers of weighted graphs of size $O(n\log…
We consider problems of the following type: given a graph $G$, how many edges are needed in the worst case for a sparse subgraph $H$ that approximately preserves distances between a given set of node pairs $P$? Examples include pairwise…
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure,…
In 1990, Alon, Seymour, and Thomas gave the first balanced separator of size $O(h^{3/2}\sqrt{n})$ for any $K_h$-minor-free graph, which has had numerous algorithmic applications. They conjectured that the size of the balanced separator can…
Low-energy molecular conformers generation (MCG) is a foundational yet challenging problem in drug discovery. Denoising-based methods include diffusion and flow-matching methods that learn mappings from a simple base distribution to the…
A $k$-fault-tolerant connectivity preserver of a directed $n$-vertex graph $G$ is a subgraph $H$ such that, for any edge set $F \subseteq E(G)$ of size $|F| \le k$, the strongly connected components of $G - F$ and $H - F$ are the same.…
Given an edge-weighted directed graph $G=(V,E)$ on $n$ vertices and a set $T=\{t_1, t_2, \ldots, t_p\}$ of $p$ terminals, the objective of the \scss ($p$-SCSS) problem is to find an edge set $H\subseteq E$ of minimum weight such that $G[H]$…
We present a simple greedy procedure to compute an $(\alpha,\beta)$-spanner for a graph $G$. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is…
Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) =…
We study a new and stronger notion of fault-tolerant graph structures whose size bounds depend on the degree of the failing edge set, rather than the total number of faults. For a subset of faulty edges $F \subseteq G$, the faulty-degree…
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling…
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E…
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…