Burnt Pancake Problem: New Lower Bounds on the Diameter and New Experimental Optimality Ratios

نویسنده

  • Bruno Bouzy
چکیده

For the burnt pancake problem, we provide new values of g(−IN ), new hard positions and new experimental optimality ratios.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

on the Problem of Sorting Burnt Pancakes

The “pancake problem” is a well-known open combinatorial problem that recently has been shown to have applications to parallel processing. Given a stack of n pancakes in arbitrary order, all of different sizes, the goal is to sort them into the size-ordered configuration having the largest pancake on the bottom and the smallest on top. The allowed sorting operation is a “spatula flip”, in which...

متن کامل

New bounds on proximity and remoteness in graphs

The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

متن کامل

Fault-tolerant routing in burnt pancake graphs

Recently, researches of parallel distributed computation are getting more important. Especially, massively parallel systems are studied with enthusiasm, and many topologies have been proposed. Since multiple faulty elements are expected in a massively parallel system, fault-tolerant routing is also studied eagerly for communication avoiding the faulty elements [4,6,8]. In this study, we focus o...

متن کامل

Size-Independent Additive Pattern Databases for the Pancake Problem

The Pancake problem has become a classical combinatorial problem. Different attempts have been made to optimally solve it and/or to derive tighter bounds on the diameter of its state space for a different number of discs. Until very recently, the most successful technique for solving different instances optimally was based on Pattern Databases. Although different approaches have been tried, sol...

متن کامل

Embedding hypercubes into pancake, cycle prefix and substring reversal networks

Among Cayley graphs on the symmetric group, some that have noticeably low diameter relative to the number of generators involved are the pancake network, burnt pancake network, and cycle prefix network [1,6,7,8]. Another such Cayley graph is the star network, and constructions have been given for one-to-one and one-tomany low dilation embeddings of hypercubes into star networks [11,12,15]. For ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016