(Nearly-)tight bounds on the contiguity and linearity of cographs
نویسندگان
چکیده
منابع مشابه
(Nearly-)tight bounds on the contiguity and linearity of cographs
In this paper we show that the contiguity and linearity of cographs on n vertices are both O(log n). Moreover, we show that this bound is tight for contiguity as there exists a family of cographs on n vertices whose contiguity is Ω(log n). We also provide an Ω(log n/ log log n) lower bound on the maximum linearity of cographs on n vertices. As a by-product of our proofs, we obtain a min-max the...
متن کاملLinear-Time Constant-Ratio Approximation Algorithm and Tight Bounds for the Contiguity of Cographs
In this paper we consider a graph parameter called contiguity which aims at encoding a graph by a linear ordering of its vertices. We prove that the contiguity of cographs is unbounded but is always dominated by O(logn), where n is the number of vertices of the graph. And we prove that this bound is tight in the sense that there exists a family of cographs on n vertices whose contiguity is Ω(lo...
متن کاملTight lower bounds for adaptive linearity tests
Linearity tests are randomized algorithms which have oracle access to the truth table of some function f , which are supposed to distinguish between linear functions and functions which are far from linear. Linearity tests were first introduced by Blum, Luby and Rubenfeld in [BLR93], and were later used in the PCP theorem among other applications. The quality of a linearity test is described by...
متن کاملNearly Tight Bounds on $\ell_1$ Approximation of Self-Bounding Functions
We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube {0, 1}n. Informally, a function f : {0, 1}n → R is self-bounding if for every x ∈ {0, 1}n, f(x) upper bounds the sum of all the n marginal decreases in the value of the function at x. Self-bounding functions include such well-known classes of functions as submo...
متن کاملNearly Tight Bounds for Wormhole Routing
We present nearly tight bounds f o r wormhole routing on Butterfly networks which indicate it is fundamentally different from store-and-forward packet routing. For instance, consider the problem of routing N log N (randomly generated) log N length messages from the inputs to the outputs of an N input Butterfly. We show that with high probability that this must take time at least fl(10g3 N/(logl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.11.036