Math 233 A : Non - constructive methods in combinatorics Instructor : Jan Vondrák
نویسنده
چکیده
Running a recursive algorithm on this expression still gives an exponential worst-case running time. Additionally, there is no hope to only explore a local neighborhood of a single vertex u with this recurrence to run an approximate calculation, because the quantity q̆S in some sense indeed depends on all of S. As in the proof of Shearer’s Lemma, however, we can rearrange the recurrence to obtain a telescoping product
منابع مشابه
Math 233 A : Non - constructive methods in combinatorics Instructor :
A hypergraph is just a set system: there is some ground set V , and the hypergraph is just some collection of subsets, F ⊆ 2V . The goal is to color the elements of V red and blue so that no element of F is monochromatic. Let’s assume that the hypergraph is k-uniform, namely that all sets in F have cardinality k. One natural approach is to color randomly: we independently assign each vertex the...
متن کاملMath 233 A : Non - constructive methods in combinatorics Instructor :
Here Ei are subsets of a probability space Ω (typically a finite set), and E i = Ω \ Ei denotes the complementary event for each i. If ∑ i P[Ei] < 1, then the above inequality clearly follows, by the “union bound”. However, this is often not a strong enough tool, since the sum ∑ i P[Ei] may be much larger than 1 even if the events can be avoided. A weaker constraint on the individual probabilit...
متن کاملMath 233 : Non - constructive methods in combinatorics
Proof: Let G be a dependency graph for {Ei} with maximum degree d, and let p = (d− 1)d−1/dd. We may assume that G is connected, since otherwise the problem reduces to a collection of independent problems. For G connected, we can find an ordering of vertices (v1, . . . , vn) such that each vi, i ≥ 2, has degree at most d − 1 among {vi, . . . , vn}. (However, this is not possible to arrange for v...
متن کاملSenior Seminar Topics
2006-2007 Discrete Probability Instructor: Abra Brisbin (CAM) The first few days introduced set theory and combinatorics. After that, they turned to probability distributions, expected value, and independence. In the second half of the course, they worked on conditional probability, Bayes’ Theorem, the Monte Carlo method, and Markov chains. Throughout the course, they tackled questions involvin...
متن کاملOptimization via enumeration: a new algorithm for the Max Cut Problem
We present a polynomial time algorithm to find the maximum weight of an edge-cut in graphs embeddable on an arbitrary orientable surface, with integral weights bounded in the absolute value by a polynomial of the size of the graph. The algorithm has been implemented for toroidal grids using modular arithmetics and the generalized nested dissection method. The applications in statistical physics...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2018