Alexander Schrijver

Alexander Schrijver
Renate Schmid · CC BY-SA 2.0 de · source
Name	Alexander Schrijver
Birth date	1958
Birth place	Netherlands
Nationality	Dutch
Fields	Combinatorics; Optimization; Graph theory; Algorithms
Alma mater	Universiteit van Amsterdam
Doctoral advisor	Martin Grötschel

Alexander Schrijver is a Dutch mathematician and computer scientist noted for foundational work in combinatorial optimization, graph theory, polyhedral combinatorics, and algorithmic complexity. He has held academic and research positions in leading European institutions and published influential monographs and papers that connect structural graph theory with linear programming, integer programming, and semidefinite programming. His work has impacted the development of algorithms for network design, matching theory, matroid theory, and optimization software.

Early life and education

Schrijver was born in the Netherlands and studied mathematics at the Universiteit van Amsterdam, where he completed doctoral studies under the supervision of Martin Grötschel. During his formative years he interacted with researchers from institutions such as Eindhoven University of Technology, Leiden University, Rotterdam, and research groups affiliated with CWI and EUR. His doctoral work and early collaborations connected him to prominent figures and centers including László Lovász, Miklós Ajtai, Neil Robertson, Paul Seymour, and the research culture fostered by offices such as Bell Labs and laboratories like INRIA.

Academic career and positions

Schrijver's academic appointments included roles at the Centrum Wiskunde & Informatica, the Universiteit van Amsterdam, and visiting positions at institutions such as Cornell University, Princeton University, Massachusetts Institute of Technology, Stanford University, and University of California, Berkeley. He collaborated with scholars from IBM Research, Microsoft Research, ETH Zurich, EPFL, and TU Eindhoven. Schrijver served on program committees for conferences including STOC, FOCS, SODA, ICALP, ESA, and IPCO, and held editorial responsibilities for journals like Journal of Combinatorial Theory, Mathematics of Operations Research, SIAM Journal on Computing, and Annals of Mathematics. He has been involved with societies such as the Royal Dutch Academy of Arts and Sciences, European Mathematical Society, SIAM, and ACM.

Research contributions and major results

Schrijver made seminal contributions to matching theory building on work by Jack Edmonds and Kőnig. He advanced polyhedral descriptions of matching and matroid polytopes following themes from George Dantzig and Richard Karp. His research on T-joins, blossoms, and algorithms for weighted matching connected to results by Edmonds (mathematician), Claude Berge, and József Beck. In polyhedral combinatorics he resolved structural problems related to the matching polytope, the Tutte matrix, and facets inspired by work of Hassler Whitney and William Tutte. Schrijver's breakthroughs in cutting-plane methods and integer programming were informed by ideas from Ralph Gomory and Egerváry, and influenced branch-and-cut algorithms used in industrial solvers developed by teams including FICO and Gurobi.

He established polynomial-time algorithms and complexity classifications for network flows, matroid intersection, and submodular function minimization, extending contributions of Jack Edmonds and László Lovász. Schrijver produced deep results on integrality of polyhedra, total dual integrality, and unimodularity connected to theories by Paul D. Seymour and Neil Robertson. His work on semidefinite programming and approximation algorithms related to landmarks by Michel Goemans and Shmuel Safra, and he contributed to derandomization techniques echoing Noga Alon and Mihir Bellare.

He authored constructive proofs and algorithmic implementations that tied combinatorial structure to linear and semidefinite relaxations, influencing practical algorithms for traveling salesman problem, graph coloring, maximum cut problem, and steady-state network design. Collaborations and cross-fertilization involved researchers such as Alexander V. Karzanov, Vladimir Kolmogorov, András Frank, and Egon Balas.

Awards and honors

Schrijver's accolades include major recognitions from national and international bodies such as membership of the Royal Netherlands Academy of Arts and Sciences, prizes akin to the Fulkerson Prize, invitations to speak at the International Congress of Mathematicians, and awards given by societies like SIAM and the European Mathematical Society. He has been honored with fellowships and visiting scholar positions at institutions such as Institute for Advanced Study, Mathematical Sciences Research Institute, and research chairs sponsored by organizations like Nederlandse Organisatie voor Wetenschappelijk Onderzoek and European Research Council.

Selected publications

Schrijver authored influential texts and papers including a comprehensive monograph on combinatorial optimization that synthesizes topics from linear programming and integer programming to graph algorithms, and articles in journals alongside authors like Martin Grötschel and László Lovász. His books stand alongside classics by George Dantzig, Jack Edmonds, Richard Karp, László Lovász, and Miklós Simonovits in shaping the field. Key papers address matching theory, matroid intersection, total dual integrality, and algorithmic aspects that influenced subsequent results by Éva Tardos, Sanjeev Arora, Umesh Vazirani, and Éric Tardos.

Legacy and influence on combinatorial optimization

Schrijver's legacy permeates modern combinatorial optimization through foundational theory and implementable algorithms used in academic research and industry settings such as telecommunications firms, logistics companies, and financial institutions that rely on optimization software developed by teams including FICO, IBM, and Gurobi. His textbooks and papers are standard references in courses at ETH Zurich, Princeton University, University of Cambridge, Oxford University, and MIT. Through students, collaborators, and citations linking to work by László Lovász, Jack Edmonds, Paul Seymour, Neil Robertson, and Martin Grötschel, his influence continues to shape new developments in approximation algorithms, polyhedral theory, and complexity theory represented in venues such as STOC, FOCS, and SODA.

Category:Dutch mathematicians Category:Combinatorial optimization