Assume we inspect a specimen represented as a collection of points and our task is to learn a physical value associated with each point. However, performing a direct measurement is impossible since it damages the specimen. The alternative is to ...

This paper initiates the study of the maximum neighborhood degree realization problem. Given a sequence D = ( d 1 , … , d n ) of non-negative integers, the goal is to construct a simple graph with vertices v 1 , … , v n such that for ...

The paper concerns the question of which properties of a graph are already determined by its degree sequence. The classic degree realization problem asks to characterize graphic sequences, i.e., sequences of positive integers, which ...

• A new approach of formation control is proposed for a multi-agent system with target geometric configuration.

Swarming motility arise very naturally in biological, physical, social sciences, etc. However, how to realize artificial intelligent self-organizing behavior is still an interesting and challenging task, especially for formation ...

This paper presents and studies a generalization of the microscopic image reconstruction problem (MIR) introduced by Frosini and Nivat (2007) and Nivat (2002). Consider a specimen for inspection, represented as a collection of points ...

Consider the following natural variation of the degree realization problem. Let G = ( V , E ) be a simple undirected graph of order n. Let f ∈ R ≥ 0 n be a vector of vertex requirements, and let w ∈ R ≥ 0 n be a vector of provided ...

Consider the following natural variation of the degree realization problem. Let $G=(V,E)$ be a simple undirected graph of order n. Let $f\in {\mathbb{R}}_{\ge 0}^n$ be a vector of vertex requirements, and let $w\in {\mathbb{R}}_{\ge 0}^n$ be a vector of provided services at the vertices. Then w...${}_{}{}_{}{}_{}$$$

Assume that we inspect a specimen represented as a collection of points. The points are typically organized on a grid structure in 2D- or 3D-space, and each point has an associated physical value. The goal of the inspection is to determine these ...${\mathbb{}}^{}$${}_{}$${\mathcal{}}_{}{}_{}{}_{}$$$$\mathcal{}{\mathcal{}}_{}$$\mathcal{}$$$$\mathcal{}$${}_{}$$$$\mathcal{}$

The classical Erdös-Gallai theorem kicked off the study of graph realizability by characterizing degree sequences. We extend this line of research by investigating realizability of directed acyclic graphs (DAGs) given both a local constraint via ...

For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings, ...

We consider the problem of positioning a cloud of points in the Euclidean space źd, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and reconstruction of ...

Mighton (2008) [5] recently gave a new characterization of graphic matroids. This note combines Mighton's approach with a result of Cunningham (1982) [4] to provide a shorter, more direct proof of Mighton's result.

We formulate the sensor network localization problem as finding the global minimizer of a quartic polynomial. Then sum of squares (SOS) relaxations can be applied to solve it. However, the general SOS relaxations are too expensive to implement for ...

In the method for graph realization from a matrix proposed by Mayeda, there could be the difficulty of the formation of a pair of M submatrices if there exist multiple H submatrices. The connectivity of the connected blocks is investigated and a method ...

We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove ...