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We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush-Kuhn-Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
We present a randomized algorithm that, given a constant $\epsilon > 0$, outputs a proper $(1+\epsilon)\Delta$-edge-coloring of an $m$-edge simple graph $G$ of maximum degree $\Delta \geq 1/\epsilon$ in $O(m)$ time with high probability.…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In the model of \emph{local computation algorithms} (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related…
We deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a $(p,q)$-Laplacian system with a parameter on locally finite graphs.The main tool is an abstract critical points…