Euclidean distance matrices, semidefinite programming and sensor network localization | Zendy

Abdo Y. Alfakih | Zendy; Miguel F. Anjos | Zendy; Veronica Piccialli | Zendy; Henry Wolkowicz | Zendy

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Euclidean distance matrices, semidefinite programming and sensor network localization

Author(s) -

Abdo Y. Alfakih,

Miguel F. Anjos,

Veronica Piccialli,

Henry Wolkowicz

Publication year - 2011

Publication title -

portugaliae mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 14

eISSN - 1662-2758

pISSN - 0032-5155

DOI - 10.4171/pm/1881

Subject(s) - semidefinite programming , mathematics , euclidean geometry , embedding , regular polygon , dimension (graph theory) , context (archaeology) , convex optimization , euclidean distance matrix , combinatorics , discrete mathematics , mathematical optimization , computer science , geometry , artificial intelligence , paleontology , biology

The fundamental problem of distance geometry involves the characterization and\udstudy of sets of points based only on given values of some or all of the distances between\udpairs of points. This problem has a wide range of applications in various areas of mathe-\udmatics, physics, chemistry, and engineering. Euclidean distance matrices play an important\udrole in this context by providing elegant and powerful convex relaxations. They play an\udimportant role in problems such as graph realization and graph rigidity. Moreover, by\udrelaxing the embedding dimension restriction, these matrices can be used to approximate\udthe hard problems e‰ciently using semidefinite programming. Throughout this survey we\udemphasize the interplay between these concepts and problems. In addition, we illustrate\udthis interplay in the context of the sensor network localization problem

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