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We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…
The aim of this paper is to present an algorithm which gives all the possible paths that start from a specific node to another of a weighted multi-graph. This algorithm is intended to be applied for the direct topological method.
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
We consider the problem of finding a Hamiltonian path with precedence constraints in the form of a partial order on the vertex set. This problem is known as Partially Ordered Hamiltonian Path Problem (POHPP). Here, we study the complexity…
We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…
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…
We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we…
The trapping problem on graph (or network) as a typical focus of great interest has attracted more attention from various science fields, including applied mathematics and theoretical computer science, in the past. Here, we first study this…
Many applications, including provenance and some analyses of social networks, require path-based queries over graph-structured data. When these graphs contain sensitive information, paths may be broken, resulting in uninformative query…
While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we…
Diameter -- the task of computing the length of a longest shortest path -- is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no $O(n^{1.99})$-time algorithm even in sparse graphs [Roditty and…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Given the benefits of its low storage requirements and high retrieval efficiency, hashing has recently received increasing attention. In particular,cross-modal hashing has been widely and successfully used in multimedia similarity search…
Let $P,Q$ be longest paths in a simple graph. We analyze the possible connections between the components of $P\cup Q\setminus (V(P)\cap V(Q))$ and introduce the notion of a bi-traceable graph. We use the results for all the possible…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
Recent studies show that Graph Neural Networks (GNNs) are vulnerable to adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs to make wrong predictions. Some researches explore specific properties of clean graphs…