相关论文: A Heuristic Subexponential Algorithm to Find Paths…

We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by…

The \emph{Markov numbers} are positive integers appearing as solutions to the Diophantine equation $x^2 + y^2 + z^2 = 3xyz$. These numbers are very well-studied and have many combinatorial properties, as well as being the source of the…

The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…

We initiate the study on fault-tolerant spanners in hypergraphs and develop fast algorithms for their constructions. A fault-tolerant (FT) spanner preserves approximate distances under network failures, often used in applications like…

Graph-based semi-supervised learning is a powerful paradigm in machine learning for modeling and exploiting the underlying graph structure that captures the relationship between labeled and unlabeled data. A large number of classical as…

Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$ for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$. In this paper,…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

Grid graphs, and, more generally, $k\times r$ grid graphs, form one of the most basic classes of geometric graphs. Over the past few decades, a large body of works studied the (in)tractability of various computational problems on grid…

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov…

Graphs have been commonly used to model many applications. A natural problem which abstracts applications such as itinerary planning, playlist recommendation, and flow analysis in information networks is that of finding the heaviest path(s)…

A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and…

Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…

A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…

We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition…

The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after…

Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…

We present an effective heuristic for the Steiner Problem in Graphs. Its main elements are a multistart algorithm coupled with aggressive combination of elite solutions, both leveraging recently-proposed fast local searches. We also propose…

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct pairs. We determine, with an exception of two cases, the complexity of the…

Several `edge-discovery' applications over graph-based data models are known to have worst-case quadratic time complexity in the nodes, even if the discovered edges are sparse. One example is the generic link discovery problem between two…