TY - BOOK ID - 7689405 TI - Sparsity : Graphs, Structures, and Algorithms AU - Nešetřil, Jaroslav. AU - Ossona de Mendez, Patrice. PY - 2012 VL - 28 SN - 3642427766 3642278744 3642278752 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Combinatorial analysis. KW - Computational complexity. KW - Linear systems. KW - Sparse matrices. KW - Sparse matrices KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebra KW - Combinatorics KW - Spare matrix techniques KW - Mathematics. KW - Algorithms. KW - Computer science KW - Convex geometry. KW - Discrete geometry. KW - Mathematical logic. KW - Combinatorics. KW - Discrete Mathematics in Computer Science. KW - Convex and Discrete Geometry. KW - Mathematical Logic and Foundations. KW - Algorithm Analysis and Problem Complexity. KW - Mathematical analysis KW - Matrices KW - Discrete groups. KW - Logic, Symbolic and mathematical. KW - Computer software. KW - Software, Computer KW - Computer systems KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Groups, Discrete KW - Infinite groups KW - Complexity, Computational KW - Electronic data processing KW - Machine theory KW - Discrete mathematics KW - Computer science—Mathematics. KW - Convex geometry . KW - Algorism KW - Arithmetic KW - Geometry KW - Combinatorial geometry KW - Foundations UR - https://www.unicat.be/uniCat?func=search&query=sysid:7689405 AB - This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010. ER -