We describe a new technique for graph layout subject to constraints. Compared to previous techniques the proposed method is much faster and scalable to much larger graphs. For a graph with n nodes, m edges and c constraints it computes incremental layout in time O(n logn+m+ c) per iteration. Also, it supports a much more powerful class of constraint: inequalities or equalities over the Euclidea...

We explore the connection between locally constrained graph homomorphisms and degree matrices arising from an equitable partition of a graph. We provide several equivalent characterizations of degree matrices. As a consequence we can efficiently check whether a given matrix M is a degree matrix of some graph and also compute the size of a smallest graph for which it is a degree matrix in polyno...

This paper presents a novel way of manipulating the initial conditions in the consensus equation such that a constrained agreement problem is solved across a distributed network of agents, particularly for a network represented by a tree graph. The presented method is applied to the problem of coordinating multiple pendula attached to mobile bases. The pendula should move in such a way that the...

Given observations about a collection of nodes, the goal of graph reconstruction is to predict a set of edges that connect the nodes in a realistic fashion. A number of similar formulations of the problem have been introduced across research areas, notably social sciences, epidemiology and biology. What is common across domains is the understanding that interesting properties of the system are ...

Given an undirected graph on n vertices with weights on its edges, Min WCF(p) consists of computing a covering forest of minimum weight such that each of its tree components contains at least p vertices. It has been proved that Min WCF(p) is NP -hard for any p ≥ 4 (Imielinska et al., 1993) but (2 − 1 n )-approximable (Goemans and Williamson, 1995). While Min WCF(2) is polynomial-time solvable, ...

In 2008 Amanatidis, Green and Mihail introduced the Joint Degree Matrix (JDM) model to capture the fundamental difference in assortativity of networks in nature studied by the physical and life sciences and social networks studied in the social sciences. In 2014 Czabarka proposed a direct generalization of the JDM model, the Partition Adjacency Matrix (PAM) model. In the PAM model the vertices ...

In this paper, a space partition method called “Label Constrained Graph Partition” (LCGP) is presented to solve the Sample-InterweavingPhenomenon in the original space. We first divide the entire training set into subclasses by means of LCGP, so that the scopes of subclasses will not overlap in the original space. Then “Most Discriminant Subclass Distribution” (MDSD) criterion is proposed to de...

Background: Bacterial DNA has immunostimulatory effects on different types of immune cells such as dendritic cells (DCs). Application of DCs as a cellular adjuvant represents a promising approach in the immunotherapy of infectious disease and cancers. Objectives: To investigate the effect of tumor antigen pulsed DCs in the presence of CpG-1826 in treatment of a murine model of cancer. Methods: ...

A divide-and-merge approach is introduced for automatic generation of high-level, discrete contact state space, represented as contact state graphs, between two contacting polyhedral solids from their geometric models. Based on the fact that a contact state graph is the union of the subgraphs called a goal-contact relaxation (GCR) graph, the approach consists of algorithms (1) to generate a com...