Handbook of Discrete and Computational Geometry

"Discrete and computational geometry is a thriving field, and the collective knowledge represented in this third edition of the Handbook is evidence of this. Twenty years have passed since the publication of the first edition [Handbook of discrete and compu-tational geometry, CRC Press Ser. Discrete Math. Appl., CRC, Boca Raton, FL, 1997; MR1730156], and since then, the area has seen a tremendous growth due in part to the influence of both the first and second editions [Handbook of discrete and computational geometry, Discrete Math. Appl. (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2004; MR2082993] of the Handbook. The new edition can be expected to serve a similar purpose for future generations of researchers and practitioners.

The third edition has a new co-editor, Csaba D. T´oth, who joins the two editors of the previous editions, Jacob E. Goodman and Joseph O’Rourke.

The third edition of the Handbook has been substantially revised. The addition of almost 400 pages has resulted in a volume of well over 1900 pages. Fifty-eight out of the sixty-five chapters of the second edition have been updated (sometimes with a slightly revised title), many of them by the original authors, others in collaboration with new co-authors. Ten new chapters have been added, for an overall count of sixty-eight chapters.

Five new chapters on computational topology and its applications have been added, including four in a new section on “Combinatorial and Computational Topology”. These deal with random simplicial complexes, computational topology of graphs on surfaces, persistent homology, high-dimensional topological data analysis, and geometry and topology of genomic, respectively. A new chapter on proximity algorithms, added to the section on “Algorithms and Complexity of Fundamental Geometric Objects”, provides a comprehensive treatment of relative neighborhood graphs and geometric spanners. There also are two new chapters in the section on “Computational Techniques”: on epsilon-approximations and epsilon-nets and on coresets and sketches, respectively. Finally, two more new chapters in the section on “Applications of Discrete and Compu-tational Geometry” describe recent advances in rigidity theory and concern rigidity of symmetric frameworks and global rigidity, respectively.

The new version remains an invaluable resource for anyone interested in discrete and computational geometry and in related areas, including specialists and non-specialists. The Handbook continues to be an attractive one-stop reference book."

- Egon Schulte - Mathematical Reviews Clippings - May 2019