Related papers: Decremental Matching in General Graphs
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an $O(m \sqrt{n})$-time algorithm for the problem, where $n$ and $m$…
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph $G$ and a source node $s$ the goal is to maintain shortest distances between $s$ and all other nodes in $G$ under a sequence of…
We give an $\tilde{O}(n^{7/5} \log (nC))$-time algorithm to compute a minimum-cost maximum cardinality matching (optimal matching) in $K_h$-minor free graphs with $h=O(1)$ and integer edge weights having magnitude at most $C$. This improves…
We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…
We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…
While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a…
Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a…
Over the years, there has been extensive work on fully dynamic algorithms for classic graph problems that admit greedy solutions. Examples include $(\Delta+1)$ vertex coloring, maximal independent set, and maximal matching. For all three…
We present a dynamic algorithm for maintaining $(1+\epsilon)$-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix $A$ undergoing \emph{decreasing} updates, i.e., updates which may only decrease eigenvalues.…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
In the stochastic matching problem, we are given a general (not necessarily bipartite) graph $G(V,E)$, where each edge in $E$ is realized with some constant probability $p > 0$ and the goal is to compute a bounded-degree (bounded by a…
Temporal graphs are graphs where the topology and/or other properties of the graph change with time. They have been used to model applications with temporal information in various domains. Problems on static graphs become more challenging…
We consider the problem of maintaining a $(1-\epsilon)$-approximation to the densest subgraph (DSG) in an undirected multigraph as it undergoes edge insertions and deletions (the fully dynamic setting). Sawlani and Wang [SW20] developed a…