相关论文: Two polynomial algorithms for special maximum matc…

A common subgraph of two graphs $G_1$ and $G_2$ is a graph that is isomorphic to subgraphs of $G_1$ and $G_2$. In the largest common subgraph problem the task is to determine a common subgraph for two given graphs $G_1$ and $G_2$ that is of…

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…

We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…

We present a polynomial-time $\frac{3}{2}$-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem…

We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…

Several papers have achieved time $O(\sqrt n m)$ for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds'…

Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…

In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…

Induced bipartite subgraphs of maximal vertex cardinality are an essential concept for the analysis of graphs. Yet, discovering them in large graphs is known to be computationally hard. Therefore, we consider in this work a weaker notion of…

Matching algorithms are used routinely to match donors to recipients for solid organs transplantation, for the assignment of medical residents to hospitals, record linkage in databases, scheduling jobs on machines, network switching, online…

We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…

We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is…

In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has…

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or…

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility…

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are…