On Shallit’s Minimization Problem
نویسندگان
چکیده
In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum rational function $$n$$ variables defined as sum special form whose number terms is order $$n^2$$ $$n\to\infty$$ . Of particular interest second term this (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating constant, which contained some auxiliary sequences with certain properties monotonicity. However, rigorous justification properties, necessary assert convergence process, replaced by reference numerical data. present paper, gaps proof are filled on basis analysis trajectories two-dimensional dynamical system discrete time corresponding points -sums. addition, sharp exponential estimate remainder asymptotic formula obtained.
منابع مشابه
On crossing minimization problem
In this paper we consider a problem related to global routing post-optimization: the crossing minimization problem (CMP). Given a global routing representation, the CMP is to minimize redundant crossings between every pair of nets. In particular, there are two kinds of CMP: constrained CMP (CCMP) and unconstrained CMP (UCMP). These problems have been studied previously in Groe89], where an O(m ...
متن کاملOnline Minimization Knapsack Problem
In this paper, we address the online minimization knapsack problem, i. e., the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack. We study the removable model, where it is allowed to remove old items from the knapsack in order to accept a new item. We obtain the following results. (i) We propose an 8-competitive deterministic algorit...
متن کاملOn stretch minimization problem on unit strip paper
For a given mountain-valley pattern of equidistant creases on a long strip paper, there are many folded states consistent with the pattern. Among these folded states, we like to fold a paper so that the number of the paper layers between each pair of hinged paper segments is minimized. We first formalize this problem as optimization problem. The complexity of the problem is not known. In this p...
متن کاملThe graph bisection minimization problem
A method of determining a lower bound for the graph bisection minimization problem is described. The bound is valid for weigthed graphs with edge and node weights. The approach is based on Lagrangian relaxation and was previously used for determining an upper bound on the independence number of a graph. The determination of the lower bound is done by solving a quadratic programming problem. A c...
متن کاملEmissions Minimization Vehicle Routing Problem
Environmental, social and political pressures to limit the impacts associated with green house gas (GHG) emissions are mounting rapidly. To date there has been no or limited research which seeks to reduce emissions as the primary objective of a routing problem despite the fast growth and high impact of commercial vehicles. In the capacitated vehicle routing problem with time windows (VRPTW), it...
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: Mathematical Notes
سال: 2021
ISSN: ['1573-8876', '0001-4346', '1067-9073']
DOI: https://doi.org/10.1134/s0001434621090078