相关论文: Lattices and maximum flow algorithms in planar gra…

A multiflow in a planar graph is uncrossed if its support paths do not cross. Recently such flows have played a role in approximation algorithms for maximum disjoint paths in "fully-planar" instances, where the combined supply-demand graph…

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine…

Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…

We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…

Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…

We propose a simple and computationally efficient method for dense subgraph discovery, which is a classic problem both in theory and in practice. It is well known that dense subgraphs can have strong correlation with structures of interest…

We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…

Lattice-linear systems allow nodes to execute asynchronously. We introduce eventually lattice-linear algorithms, where lattices are induced only among the states in a subset of the state space. The algorithm guarantees that the system…

Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…

A modulator of a graph G to a specified graph class H is a set of vertices whose deletion puts G into H. The cardinality of a modulator to various tractable graph classes has long been used as a structural parameter which can be exploited…

We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…

We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in…

Graph neural networks (GNNs) have found application for learning in the space of algorithms. However, the algorithms chosen by existing research (sorting, Breadth-First search, shortest path finding, etc.) usually align perfectly with a…

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can…

Every irreducible outer automorphism of the free group of rank r is topologically represented by an irreducible train track map $f$ on some graph $\Gamma$ of rank r. Moreover, $f$ can always be written as a composition of folds and a graph…

Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…

To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured…

Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely…

Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the lattice of congruences on a graph inverse semigroup is upper semimodular but not lower…