Related papers: Towards a better approximation for sparsest cut?
Expander decompositions form the basis of one of the most flexible paradigms for close-to-linear-time graph algorithms. Length-constrained expander decompositions generalize this paradigm to better work for problems with lengths, distances…
In this note, we revisit the recursive random contraction algorithm of Karger and Stein for finding a minimum cut in a graph. Our revisit is occasioned by a paper of Fox, Panigrahi, and Zhang which gives an extension of the Karger-Stein…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider this problem in the setting of local algorithms: one wants to quickly determine whether a given edge $e$ is in a specific spanning tree,…
Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the…
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
Guruswami and Sinop give a $O(1/\delta)$ approximation guarantee for the non-uniform Sparsest Cut problem by solving $O(r)$-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and…
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with $m$ edges and $n$ nodes undergoing edge deletions, we provide four new approximate…
We give the first fully dynamic algorithm which maintains a $(1-\epsilon)$-approximate densest subgraph in worst-case time $\text{poly}(\log n, \epsilon^{-1})$ per update. Dense subgraph discovery is an important primitive for many…
We introduce the $st$-cut version the Sparsest-Cut problem, where the goal is to find a cut of minimum sparsity among those separating two distinguished vertices $s,t\in V$. Clearly, this problem is at least as hard as the usual (non-$st$)…
We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Our algorithm achieves an approximation factor of O(f(g)) on graphs…
In this paper, we present a new randomized $O(1)$-approximation algorithm for the All-Pairs Shortest Paths (APSP) problem in weighted undirected graphs that runs in just $O(\log \log \log n)$ rounds in the Congested-Clique model. Before our…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
We present a randomized algorithm for the single-source shortest paths (SSSP) problem on directed graphs with arbitrary real-valued edge weights that runs in $n^{2+o(1)}$ time with high probability. This result yields the first almost…
In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…