Related papers: How to Secure Matchings Against Edge Failures
For any given metric space, obtaining an offline optimal solution to the classical $k$-server problem can be reduced to solving a minimum-cost partial bipartite matching between two point sets $A$ and $B$ within that metric space. For…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
This paper explores combinatorial optimization for problems of max-weight graph matching on multi-partite graphs, which arise in integrating multiple data sources. Entity resolution-the data integration problem of performing noisy joins on…
We investigate the problem of simultaneously dominating all spanning trees of a given graph. We prove that on 2-connected graphs, a subset of the vertices dominates all spanning trees of the graph if and only if it is a vertex cover. Using…
We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming fashion. We analyze a variant of the previously best-known…
We consider the maximum bipartite matching problem in stochastic settings, namely the query-commit and price-of-information models. In the query-commit model, an edge e independently exists with probability $p_e$. We can query whether an…
A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
We show that finding minimally intersecting $n$ paths from $s$ to $t$ in a directed graph or $n$ perfect matchings in a bipartite graph can be done in polynomial time. This holds more generally for unimodular set systems.
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We study three new versions of the All-Ones Problem and the Minimum All-Ones Problem. The original All-Ones Problem is simply called the Vertex-Vertex Problem, and the three new versions are called the Vertex-Edge Problem, the Edge-Vertex…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm one by one, along with its…