The problem of finding a longest increasing subsequence (LIS) is a well known task in sequence processing. There are many variants of the basic task. We discuss a recently introduced variant of LIS, a minimal height longest increasing subsequence problem and propose a new algorithm for it, which improves its time complexity. Moreover, we define a family of similar problems and introduce algorit...

Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. We discuss the “hydrodynamical approach” to the analysis of the limit behavior, which probably started with Hammersley (1972), and was subsequently further developed by several authors. We also give two proofs of an exact (non-a...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

A revenue sharing contract is one of the mechanisms that coordinate decision makers in a decentralized supply chain toward the consensual goal. The transfer prices between different echelons in the supply chain influence the total supply chain profits. The study aims to explore various transfer pricing heuristics on the supply chain coordination in terms of the supply chain profits and their in...

The objective of the paper is to study how wholesale price and revenue sharing contracts affect operations and marketing decisions in a supply chain under different dynamic informational structures. We suggest a differential game model of a supply chain consisting of a manufacturer and a single retailer that agree on the contract parameters at the outset of the game. The model includes key oper...

This work explores the impact of quick response on supply chain performance for various supply chain structures with strategic customer behavior. By investigating pricing and inventory decisions in decentralized supply chains under revenue-sharing contracts and in centralized supply chains, we study the performance of four various systems and compare the value of quick response in different sup...

We explore coordination issues of a two-echelon supply chain, consisting of a distributor and a retailer. The effect of revenue-sharing contract mechanism is examined under stock-time-pricesensitive demand rate. First, we investigate relationships between distributor and retailer under noncooperative distributor-Stackelberg games. Thenwe establish analytically that revenue sharing contact is ab...

Th e quest for improved self-revenue generation and reduction of the fi nancial burden on government prompted the adoption of public private partnership (PPP) in the management of South African National Parks (SANParks). Accordingly, this paper examined the revenue and conservation implication of PPP in SANParks. Using a statistical t-test of diff erence in means, before and within the PPP, res...