相关论文: Graphical Newton
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
The \emph{$r$-neighbourhood complexity} of a graph $G$ is the function counting, for a given integer $k$, the largest possible number, over all vertex-subsets $A$ of size $k$, of subsets of $A$ realized as the intersection between the…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
In this paper, we present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of…
Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor's way of measuring the local crookedness of a Jordan curve…
The Fibonacci dimension fdim(G) of a graph G is introduced as the smallest integer f such that G admits an isometric embedding into Gamma_f, the f-dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of…
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…
We investigate the computational complexity of some problems in three-dimensional topology and geometry. We show that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. Using similar ideas, we show…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…