arXiv subjects

Alexander Ponomarenko

Publications and source records attributed to Alexander Ponomarenko.

7 recordsLinked to original sources

arXiv2026

Tuning Dispatch Thresholds for Fixed Last-Mile Routes: A Simulation-Based Pareto Analysis of a Production Policy

Many parcel networks dispatch vehicles on \emph{fixed routes} using a simple load-accumulation rule: a truck leaves the depot for a fixed route as soon as the volume (or item count) waiting for that route crosses a threshold. The threshold is usually parameterised as an affine function of route length, $τ_r=β+γ\,d_r$, and the pair $(β,γ)$ is chosen once and frozen into production. This paper studies how good that frozen choice actually is, treating the question as a data-intensive, data-driven decision-making problem over a full month of real operational flow. Using a discrete-event simulator that replays the recorded arrival stream and reconstructs every trip, we sweep the $(β,γ)$ design space, evaluate the two competing objectives -- company operating cost and average parcel lead time -- and recover the Pareto frontier of efficient policies for two deployed variants (volume-triggered and item-count-triggered). The two policies turn out to be in strikingly different states of tune. The volume-threshold configuration lies on its own Pareto frontier: the simulator finds no $(β,γ)$ pair that strictly dominates it, so the deployed policy is \emph{already Pareto-efficient} -- an unusual positive audit result. The item-count configuration is the opposite: it is dominated by a concrete simulated configuration that is both faster and cheaper, and the available cost saving at equal lead time is about \num{5.0}\,\pct{}. We trace the item-count policy's inefficiency to a base that is too large and a length coefficient that is too small for the deployed truck capacity, and show that a \emph{steeper} threshold -- lower base, higher slope -- is preferable. Because the remedy is a two-scalar reconfiguration, the analysis converts directly into an actionable, zero-capital recurring saving.

cs.CE↗

arXiv2026

A Benchmark Generator of Realistic Logistic Transport Networks with Nonlinear Edge Costs and Transshipment Capacities

Routing many commodities through a logistic network at minimum joint cost of vehicle movements and transshipment at intermediate storages becomes substantially harder -- and substantially more realistic -- once two features are present together: edge costs that are \emph{nonlinear} in the transported volume, because freight travels in fixed-capacity vehicles, and \emph{hard upper bounds} on the volume reloaded at each storage. No public benchmark captures this combination, and the locations of commercial distribution centres are proprietary. We close this gap with a parameterised generator of synthetic logistic networks, calibrated on real road graphs of nine European countries, five U.S.\ states and the European part of Russia extracted from OpenStreetMap. The generator reproduces the structural signatures of upper-level distribution networks -- near-planar topology, low vertex degree, short edges and large diameters -- by combining Zipf-distributed city sizes, a spatial-network budget model trading edge-building cost against routing convenience, centrality-driven storage capacities, and a doubly constrained gravity demand model. We release 35 fully synthetic instances ($10$--$150$ storages) and 15 real-geometry instances in an open, self-describing, fully reproducible file format. An empirical characterisation computed directly from the released files shows that synthetic and real-geometry instances are structurally consistent (two-sample Kolmogorov--Smirnov distances of $0.10$ on degree and edge-length distributions, with small and quantified mean deviations), and a baseline-solver study demonstrates that the corpus discriminates instance difficulty across orders of magnitude. The benchmark is a faithful, reusable testbed for the development and comparison of exact and heuristic algorithms.

physics.soc-ph↗

arXiv2026

Greedy Routing in a Sequentially Grown One-Dimensional Random Graph

We analyze greedy routing in a random graph G_n constructed on the vertex set V = {1, 2, ..., n} embedded in Z. Vertices are inserted according to a uniform random permutation pi, and each newly inserted vertex connects to its nearest already-inserted neighbors on the left and right (if they exist). This work addresses a conjecture originating from empirical studies (Ponomarenko et al., 2011; Malkov et al., 2012), which observed through simulations that greedy search in sequentially grown graphs exhibits logarithmic routing complexity across various dimensions. While the original claim was based on experiments and geometric intuition, a rigorous mathematical foundation remained open. Here, we formalize and resolve this conjecture for the one-dimensional case. For a greedy walk GW starting at vertex 1 targeting vertex n -- which at each step moves to the neighbor closest to n -- we prove that the number of steps S_n required to reach n satisfies S_n = Theta(log n) with high probability. Precisely, S_n = L_n + R_n - 2, where L_n and R_n are the numbers of left-to-right and right-to-left minima in the insertion-time permutation. Consequently, E[S_n] = 2H_n - 2 ~ 2 log n and P(S_n >= (2+c) log n) <= n^(-h(c/2) + o(1)) for any constant c > 0, with an analogous lower tail bound for 0 < c < 2, where h(u) = (1+u) ln(1+u) - u is the Bennett rate function. Furthermore, we establish that this logarithmic scaling is robust: for arbitrary or uniformly random start-target pairs, the expected routing complexity remains E[S_{s,t}] = 2 log n + O(1), closely mirroring decentralized routing scenarios in real-world networks where endpoints are chosen dynamically rather than fixed a priori.

math.CO↗

arXiv2025

Three Algorithms for Merging Hierarchical Navigable Small World Graphs

This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection and candidate collection during the merge process. We conceptualize graph merging as an iterative process with four key steps: processing vertex selection, candidate collection, neighborhood construction, and information propagation. Our experimental evaluation on the SIFT1M dataset demonstrates that IGTM and CGTM significantly reduce computational costs compared to naive approaches, requiring up to 70\% fewer distance computations while maintaining comparable search accuracy. Surprisingly, IGTM outperforms CGTM in efficiency, contrary to our initial expectations. The proposed algorithms enable efficient consolidation of separately constructed indices, supporting critical operations in modern vector databases and retrieval systems that rely on HNSW for similarity search.

cs.DS↗

arXiv2021

Overlapping community detection in networks based on link partitioning and partitioning around medoids

In this paper, we present a new method for detecting overlapping communities in networks with a predefined number of clusters called LPAM (Link Partitioning Around Medoids). The overlapping communities in the graph are obtained by detecting the disjoint communities in the associated line graph employing link partitioning and partitioning around medoids which are done through the use of a distance function defined on the set of nodes. We consider both the commute distance and amplified commute distance as distance functions. The performance of the LPAM method is evaluated with computational experiments on real life instances, as well as synthetic network benchmarks. For small and medium-size networks, the exact solution was found, while for large networks we found solutions with a heuristic version of the LPAM method.

cs.SI↗

arXiv2017

A Model of Optimal Network Structure for Decentralized Nearest Neighbor Search

One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network. A procedure in a network is called decentralized if it uses only local information about visited nodes and its neighbors. Networks, which structure allows efficient performing the nearest neighbour search by a decentralised search procedure started from any node, are of particular interest especially for pure distributed systems. Several algorithms that construct such networks have been proposed in literature. However, the following questions arise: "Are there network models in which decentralised search can be performed faster?"; "What are the optimal networks for the decentralised search?"; "What are their properties?". In this paper we partially give answers to these questions. We propose a mathematical programming model for the problem of determining an optimal network structure for decentralized nearest neighbor search. We have found an exact solution for a regular lattice of size 4x4 and heuristic solutions for sizes from 5x5 to 7x7. As a distance function we use L1 , L2 and L_inf metrics. We hope that our results and the proposed model will initiate study of optimal network structures for decentralised nearest neighbour search.

cs.DC↗

arXiv2016

Growing homophilic networks are natural navigable small worlds

Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in the majority of networks: network growth and local homophily, giving a persuasive answer how the navigation appears in real-life networks. A very simple algorithm produces hierarchical self-similar optimally wired navigable small world networks with exponential degree distribution by using only local information. Adding preferential attachment produces a scale-free network which has shorter greedy paths, but worse (power law) scaling of the information extraction locality (algorithmic complexity of a search). Introducing saturation of the preferential attachment leads to truncated scale-free degree distribution that offers a good tradeoff between these parameters and can be useful for practical applications. Several features of the model are observed in real-life networks, in particular in the brain neural networks, supporting the earlier suggestions that they are navigable.

physics.soc-ph↗