Lecture 9 — 3 March, 2014: ``9. Graph Isomorphism and the Lasserre Hierarchy.''
نویسندگان
چکیده
http://www.csc.kth.se/~lauria/sos14/ Let G and H be two graphs, we say that two graphs are isomorphic, denoted as G ≅ H, if there is a bijection π ∶ V(G) → V(H), such that {u, v} ∈ E(G) if and only if {π(u), π(v)} ∈ E(H). In this lecture, we discuss a recent paper by O’Donnell, Wright, Wu and Zhou 1 which proved the 1 R. O’Donnell, J. Wright, C. Wu, and Y. Zhou. Hardness of Robust Graph Isomorphism, Lasserre Gaps, and Asymmetry of Random Graphs, chapter 120, pages 1659– 1677. 2014 following theorem.
منابع مشابه
Graph Isomorphism and the Lasserre Hierarchy
In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp{Õ(n 13 )} (this bound was recently improved to exp{Õ(n 15 )} [5]). It has since been an open question to remove the requirement that the graph...
متن کاملSemidefinite Bounds for the Stability Number of a Graph via Sums of Squares of Polynomials
Lovász and Schrijver (SIAM J. Optim. 1:166–190, 1991) have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations; their procedure finds the stable set polytope in at most α(G) steps, where α(G) is the stability number of G. Two other hierarchies of semidefinite bounds for the stability number have been proposed by Lass...
متن کاملExploring Memory Hierarchy Design with Emerging Memory Technologies
Reading a book is also kind of better solution when you have no enough money or time to get your own adventure. This is one of the reasons we show the exploring memory hierarchy design with emerging memory technologies lecture notes in electrical engineering as your friend in spending the time. For more representative collections, this book not only offers it's strategically book resource. It c...
متن کاملThe Lasserre hierarchy in Approximation algorithms
The Lasserre hierarchy is a systematic procedure to strengthen a relaxation for an optimization problem by adding additional variables and SDP constraints. In the last years this hierarchy moved into the focus of researchers in approximation algorithms as the obtain relaxations have provably nice properties. In particular on the t-th level, the relaxation can be solved in time n ) and every con...
متن کاملConstant Factor Lasserre Integrality Gaps for Graph Partitioning Problems
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such as the Uniform Sparsest Cut problem where the goal is to minimize the fraction of pairs on opposite sides of the cut that are connected by an edge, there are ...
متن کامل