相关论文: Breaking Symmetries in Graph Search with Canonizin…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has…
{\sc Vertex $(s, t)$-Cut} and {\sc Vertex Multiway Cut} are two fundamental graph separation problems in algorithmic graph theory. We study matroidal generalizations of these problems, where in addition to the usual input, we are given a…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Finding Minimal Unsatisfiable Subsets (MUSes) of binary constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely…
Effective search for graph automorphisms allows identifying symmetries in many discrete structures, ranging from chemical molecules to microprocessor circuits. Using this type of structure can enhance visualization as well as speed up…
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects…
Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded…
We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop…
The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is…
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…
A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al. 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are…
Two of the most fundamental distributed symmetry-breaking problems are that of finding a maximal independent set (MIS) and a maximal matching (MM) in a graph. It is a major open question whether these problems can be solved in constant…
While most classical NP-hard graph problems cannot be solved in time $2^{o(n)}$ on general graphs under the Exponential Time Hypothesis (ETH), many exhibit the square-root phenomenon and admit optimal algorithms running in time…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
In this study, we address the independent set enumeration problem. Although several efficient enumeration algorithms and careful analyses have been proposed for maximal independent sets, no fine-grained analysis has been given for the…
The independence number of a tree decomposition is the size of a largest independent set contained in a single bag. The tree-independence number of a graph $G$ is the minimum independence number of a tree decomposition of $G$. As shown…
For a connected graph $G=(V,E)$, a matching $M\subseteq E$ is a matching cut of $G$ if $G-M$ is disconnected. It is known that for an integer $d$, the corresponding decision problem Matching Cut is polynomial-time solvable for graphs of…