相关论文: Approximation Algorithms for the Bipartite Multi-c…

The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…

We give a simple approximation algorithm for a common generalization of many previously studied extensions of the maximum size stable matching problem with ties. These generalizations include the existence of critical vertices in the graph,…

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…

Given a connected undirected graph $\bar{G}$ on $n$ vertices, and non-negative edge costs $c$, the 2ECM problem is that of finding a $2$-edge~connected spanning multisubgraph of $\bar{G}$ of minimum cost. The natural linear program (LP) for…

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…

This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…

We introduce a $2$-approximation algorithm for the minimum total covering number problem.

In Directed Multiway Cut(Dir-MC) the input is an edge-weighted directed graph $G=(V,E)$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to find a min-weight subset of edges whose removal ensures that there…

Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…

The lifted multicut problem is a combinatorial optimization problem whose feasible solutions relate one-to-one to the decompositions of a graph $G = (V, E)$. Given an augmentation $\widehat{G} = (V, E \cup F)$ of $G$ and given costs $c \in…

We study the design of polylogarithmic depth algorithms for approximately solving packing and covering semidefinite programs (or positive SDPs for short). This is a natural SDP generalization of the well-studied positive LP problem.…

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

The current bottleneck of globally solving mixed-integer (non-convex) quadratically constrained problem (MIQCP) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are…

In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the…

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…

We consider the Demand Strip Packing problem (DSP), in which we are given a set of jobs, each specified by a processing time and a demand. The task is to schedule all jobs such that they are finished before some deadline $D$ while…

We propose an $O(\log n)$-approximation algorithm for the bipartiteness ratio of undirected graphs introduced by Trevisan (SIAM Journal on Computing, vol. 41, no. 6, 2012), where $n$ is the number of vertices. Our approach extends the…

A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…