Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1504.03170

Search algorithms for efficient logistics chains

Serge Lawrencenko·Irina A. Duborkina
View original source ↗Read source document ↗Export metadata ↓

Abstract

Logistics networks arise whenever there is a transfer of material substance or objects (such as checked baggage on international flights) as well as energy, information, or finance through links (channels). A general concept of logistics network is suggested and motivated for modeling a service of any kind supplied through links between the nodes of the network. The efficiency of a single link is defined to be the ratio of the volume of useful service at the output node to the volume of expended service at the input node of the link (for a specific period of time). Similarly, the efficiency of a chain is the ratio of the volume of service at the output to the volume of service at the input of the chain. The overall efficiency of the chain is calculated as the product of the efficiencies of its links; the more efficiency of the chain, the less are the losses in the chain. This paper introduces the notion of inadequacy of service in such a way that the overall inadequacy of a chain is equal to the sum of the inadequacies of its links. So the efficiencies are being multiplied, whereas the inadequacies are being added. Thus, the antagonistic pair (efficiency, inadequacy) appears to be analogous to the pair (reliability, entropy) in communication theory. Various possible interpretations of the proposed logistic model are presented: energy, material, information and financial networks. Four algorithms are provided for logistics chain search: two algorithms for finding the most effective chain from a specified origin to a specified destination, and two algorithms for finding the guaranteed minimum level of service between any pair of unspecified nodes in a given network. An example is shown as to how one of the algorithms finds the most efficient energy chain from the electrical substation to a specified user in a concrete energy network.

Explore related subjects

cs.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Serge Lawrencenko, Irina A. Duborkina. 2015-04-09. Search algorithms for efficient logistics chains. https://doi.org/10.12737/11889

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗