A path-finding algorithm for computing minimal-weight-matching centrosymmetry parameter

Vasily V. Pisarev

arxiv: 2605.22094 · v1 · pith:WV4HD3GGnew · submitted 2026-05-21 · ⚛️ physics.comp-ph · cond-mat.mtrl-sci

A path-finding algorithm for computing minimal-weight-matching centrosymmetry parameter

Vasily V. Pisarev This is my paper

Pith reviewed 2026-05-22 02:40 UTC · model grok-4.3

classification ⚛️ physics.comp-ph cond-mat.mtrl-sci

keywords centrosymmetry parameterminimal-weight matchingA* algorithmpath findingmolecular dynamicsatomic structure analysis

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The pith

A path-finding algorithm with A* computes the minimal-weight-matching centrosymmetry parameter equivalently to Edmonds' blossom algorithm.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates an alternative to Edmonds' blossom algorithm for calculating the centrosymmetry parameter by recasting the minimal-weight matching problem as a path-finding task solved with A*. It builds directly on the 2020 formulation that defines CSP through minimal-weight matching on the fully-connected graph of atomic neighbors. A sympathetic reader would care because the approach could make accurate CSP computation more accessible in molecular dynamics analysis packages that already contain graph-search tools. If the method works, it delivers the same matching results on the same neighbor graphs while opening a different implementation route.

Core claim

The paper presents a path-finding formulation that uses the A* algorithm to compute the minimal-weight matching required for the centrosymmetry parameter on the fully-connected graph of atomic neighbors, positioning it as an alternative to the Edmonds' blossom algorithm proposed in the 2020 Larsen formulation.

What carries the argument

A* search applied to find the minimal-weight perfect matching in the complete graph whose edge weights are interatomic distances from the neighbor list.

If this is right

The new algorithm produces identical CSP values to the original formulation when applied to the same neighbor graphs.
Molecular-dynamics packages can adopt the method using existing A* implementations instead of adding a blossom-algorithm library.
The path-finding view may allow incremental updates when only a subset of atoms moves between analysis steps.
Implementation effort shifts from matching code to defining admissible heuristics for the A* search.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Performance comparisons on systems with thousands of atoms would reveal whether A* scales better than blossom for typical neighbor-graph densities.
The method could be combined with existing graph libraries in simulation codes to reduce the barrier for adding accurate CSP analysis.

Load-bearing premise

The path-finding formulation with A* will always recover exactly the same minimal-weight matching that Edmonds' blossom algorithm finds on the fully-connected atomic-neighbor graph.

What would settle it

Run both the A* path-finding method and the blossom algorithm on the same set of atomic configurations from a crystal with known defects and check whether every resulting CSP value is identical.

read the original abstract

In 2020, Peter Larsen reported flaws in the methods for centrosymmetry parameter computation in the existing molecular dynamics and analysis packages. He proposed an intuitive an mathematically rigorous formulation for centrosymmetry parameter in terms of minimal-weight matching (MWM) on a fully-connected graph of atomic neighbors. He proposed using Edmonds' blossom algorithm for computing such a matching. In this paper, we investigate an alternative algorithm for MWM CSP computation using path finding approach and A* algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper describes an A* path-finding alternative for minimal-weight matching in centrosymmetry parameter calculations but provides limited verification of equivalence or performance gains.

read the letter

The paper takes Larsen's 2020 minimal-weight matching formulation for the centrosymmetry parameter and explores solving it with A* search instead of the blossom algorithm. It reframes the pairing of neighbors as a path-finding task on the fully connected graph of atomic positions, with a heuristic to guide the search toward low total weight. This is a reasonable algorithmic variant if the implementation is faithful to the original matching problem. The description of the state representation and search steps comes across as clear and direct. The stress-test note found no internal contradictions in how the graph is modeled, which supports treating the idea as workable on paper. The main limitation is that the work stays at the level of describing the approach and its implementation. There is no side-by-side comparison showing that A* recovers exactly the same matchings as the blossom method on real atomic configurations, and no timing results to indicate whether it runs faster or slower on typical neighbor lists. Without those checks the claimed efficiency gain remains unproven. Readers who already use the existing CSP implementation in their MD pipelines will not gain much until equivalence and speed are demonstrated. The paper is mainly of interest to developers of analysis tools who might want another option for computing the parameter. It is worth sending to peer review so that referees can examine the code and request the missing validation tests. A serious editor should ask for explicit equivalence checks before accepting.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an alternative path-finding algorithm using A* search to compute the minimal-weight matching (MWM) centrosymmetry parameter (CSP) on the fully-connected neighbor graph, as an alternative to Edmonds' blossom algorithm in the 2020 Larsen formulation.

Significance. If the A* formulation is shown to produce identical matchings and CSP values, the work could supply a new computational route for CSP evaluation in molecular dynamics. The manuscript does not include machine-checked proofs, reproducible code, or parameter-free derivations, limiting its immediate impact.

major comments (2)

[Algorithm and Implementation] The central claim requires that the path-finding formulation with A* produces exactly the same minimal-weight matching as the blossom algorithm on the complete neighbor graph. No formal equivalence proof, reduction to the MWM problem, or exhaustive numerical verification against the blossom method is provided in the algorithm description or results sections.
[Results and Validation] No benchmarks, timing comparisons, error analysis, or test cases on standard atomic configurations are reported to confirm that the computed CSP values match those from the established method.

minor comments (2)

[Method] Notation for the state space and cost function in the A* formulation should be defined more explicitly with reference to the Larsen neighbor graph.
[Introduction] The abstract and introduction would benefit from a brief statement of the expected computational complexity relative to blossom algorithm.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review of our manuscript proposing a path-finding algorithm using A* for computing the minimal-weight-matching centrosymmetry parameter. We address the major comments below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

Referee: [Algorithm and Implementation] The central claim requires that the path-finding formulation with A* produces exactly the same minimal-weight matching as the blossom algorithm on the complete neighbor graph. No formal equivalence proof, reduction to the MWM problem, or exhaustive numerical verification against the blossom method is provided in the algorithm description or results sections.

Authors: The referee correctly identifies a gap in our presentation. Our formulation derives the path-finding problem directly from the definition of the minimal-weight perfect matching on the neighbor graph, and the A* search is configured to find the optimal matching by construction. However, we did not include an explicit reduction or numerical verification in the submitted version. We will revise the manuscript to include a formal argument establishing equivalence to the MWM problem and add exhaustive numerical comparisons on various atomic configurations to confirm that the matchings and resulting CSP values are identical to those obtained with Edmonds' blossom algorithm. revision: yes
Referee: [Results and Validation] No benchmarks, timing comparisons, error analysis, or test cases on standard atomic configurations are reported to confirm that the computed CSP values match those from the established method.

Authors: We agree that empirical validation is essential. The current manuscript focuses on describing the algorithm but lacks comparative results. In the revised version, we will incorporate benchmarks including timing comparisons between the A* path-finding approach and the blossom algorithm, error analysis for CSP values, and test cases on standard configurations such as perfect crystals and defective structures to demonstrate agreement with the established method. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper proposes an alternative A* path-finding formulation for computing the minimal-weight matching in the centrosymmetry parameter (CSP) as originally defined by Larsen (2020) via Edmonds' blossom algorithm on the fully-connected neighbor graph. No equations, derivations, or predictions are presented that reduce by construction to the paper's own inputs, fitted parameters, or self-referential definitions. The manuscript focuses on describing the algorithmic implementation as an alternative without invoking load-bearing self-citations, uniqueness theorems from prior author work, or ansatzes smuggled via citation. The central claim relies on equivalence to the external Larsen formulation rather than any internal loop or renaming of known results, making the derivation chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard graph algorithms and the prior MWM formulation without introducing new fitted parameters or postulated entities.

axioms (1)

standard math A* algorithm with admissible heuristic correctly finds minimal-weight paths in the fully-connected neighbor graph.
Invoked implicitly when proposing path finding as a substitute for blossom algorithm.

pith-pipeline@v0.9.0 · 5596 in / 1076 out tokens · 36698 ms · 2026-05-22T02:40:31.729468+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 1 internal anchor

[1]

Robust benchmarking in noisy environments

Jiahao Chen and Jarrett Revels. “Robust benchmarking in noisy environ- ments”. In:arXiv e-prints, arXiv:1608.04295 (Aug. 2016). arXiv:1608.04295 [cs.PF]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[2]

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. “A Formal Basis for the Heuristic Determination of Minimum Cost Paths”. In:IEEE Transactions on Systems Science and Cybernetics4.2 (1968), pp. 100–107

work page 1968
[3]

Larsen and D.L

P.M. Larsen and D.L. Pereira.url:https://gitlab.com/stuko/ovito/- /blob/6c9b8e00a73783770ec8fb056ee527658b10004f/src/3rdparty/mwm_ csp/matching.cpp(visited on 05/17/2026)

work page 2026
[4]

Revisiting the Common Neighbour Analysis and the Cen- trosymmetry Parameter

Peter M Larsen. “Revisiting the Common Neighbour Analysis and the Cen- trosymmetry Parameter”. In:arXiv e-prints, arXiv:2003.08879 (2020).doi: 10.48550/arXiv.2003.08879. arXiv:2003.08879. HSE University Tikhonov MIEM, Moscow, Russia Email address:v.pisarev@hse.ru

work page doi:10.48550/arxiv.2003.08879 2003

[1] [1]

Robust benchmarking in noisy environments

Jiahao Chen and Jarrett Revels. “Robust benchmarking in noisy environ- ments”. In:arXiv e-prints, arXiv:1608.04295 (Aug. 2016). arXiv:1608.04295 [cs.PF]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[2] [2]

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. “A Formal Basis for the Heuristic Determination of Minimum Cost Paths”. In:IEEE Transactions on Systems Science and Cybernetics4.2 (1968), pp. 100–107

work page 1968

[3] [3]

Larsen and D.L

P.M. Larsen and D.L. Pereira.url:https://gitlab.com/stuko/ovito/- /blob/6c9b8e00a73783770ec8fb056ee527658b10004f/src/3rdparty/mwm_ csp/matching.cpp(visited on 05/17/2026)

work page 2026

[4] [4]

Revisiting the Common Neighbour Analysis and the Cen- trosymmetry Parameter

Peter M Larsen. “Revisiting the Common Neighbour Analysis and the Cen- trosymmetry Parameter”. In:arXiv e-prints, arXiv:2003.08879 (2020).doi: 10.48550/arXiv.2003.08879. arXiv:2003.08879. HSE University Tikhonov MIEM, Moscow, Russia Email address:v.pisarev@hse.ru

work page doi:10.48550/arxiv.2003.08879 2003