City-Scale Visibility Graph Analysis via GPU-Accelerated HyperBall

Alex Hodge; Melissa Barrientos Trinanes

arxiv: 2604.08374 · v1 · submitted 2026-04-09 · 💻 cs.DC

City-Scale Visibility Graph Analysis via GPU-Accelerated HyperBall

Alex Hodge , Melissa Barrientos Trinanes This is my paper

Pith reviewed 2026-05-10 16:53 UTC · model grok-4.3

classification 💻 cs.DC

keywords visibility graph analysisspace syntaxHyperBallGPU accelerationcity-scale analysisgraph compressionCUDA kernelsprobabilistic distance estimation

0 comments

The pith

GPU acceleration with HyperBall lets visibility graph analysis scale to entire cities at 239x the speed of prior tools while preserving key metric accuracy.

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

The paper shows how to overcome the computational barrier that has kept visibility graph analysis confined to small areas by replacing exhaustive all-pairs shortest-path searches with a probabilistic distance estimator. Delta-compressed graph storage, a HyperLogLog-based propagation scheme, and streaming CUDA kernels together reduce both memory footprint and per-iteration work so that radius-n computations finish in time proportional to the chosen depth rather than the full graph size. On identical edge sets generated by the same visibility algorithm used in depthmapX, the new implementation reaches 236,000 cells and 4.8 billion edges in 137 seconds, delivering a 239-fold end-to-end improvement. At the same time, visual mean depth matches the exact method with a Pearson correlation of 0.999 and only 1.7 percent median relative error when the HyperBall parameter is set to 10. This combination directly extends the radius-n workflows already standard among space-syntax practitioners, removing the practical size limit that has restricted the method to neighborhood-scale studies.

Core claim

The authors combine LEB128 delta-compressed CSR storage, HyperBall probabilistic distance estimation that lowers BFS complexity from O(N|E|) to O(D|E|2^p), and fused CUDA decode-union kernels that stream the graph over PCIe and decode in shared memory. With these components the system reproduces depthmapX edge sets exactly while achieving a 239x end-to-end speedup at 42,705 cells and completing a 236,000-cell instance (4.8 billion edges) in 137 seconds. At p=10 the resulting visual mean depth values correlate with the exact method at Pearson r=0.999 across 20 matched configurations with 1.7 percent median relative error.

What carries the argument

HyperBall, the probabilistic distance estimator based on HyperLogLog counter propagation, running inside fused CUDA decode-union kernels on delta-compressed CSR visibility graphs.

If this is right

Radius-n analyses now receive a proportional speedup because HyperBall iteration count equals the chosen depth limit instead of remaining fixed by graph diameter.
Memory-mapped compressed storage allows graphs whose edge count exceeds available RAM, opening problems with billions of visibility relations.
End-to-end city-scale workflows become practical in minutes rather than hours or days, matching the size of contemporary urban datasets.
Practitioners retain their existing radius-n settings and interpretation habits while gaining the ability to study whole metropolitan regions.

Where Pith is reading between the lines

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

The same compression-plus-probabilistic-estimation pattern could be applied to other large spatial networks where exact all-pairs distances are currently prohibitive.
Integration with streaming sensor data might allow near-real-time updates of city-wide visibility metrics during planning or emergency response.
Extending accuracy checks to additional metrics such as visual integration and choice would determine whether the current error bound holds across the full VGA suite.

Load-bearing premise

The HyperBall approximation at fixed p=10 together with the CUDA kernel implementations preserve both connectivity and metric values for every standard VGA measure, not only the single mean-depth case that was checked.

What would settle it

Compute all standard VGA metrics on a fresh 100,000-cell visibility graph with both the new tool and depthmapX and check whether any metric besides mean depth shows relative error above 5 percent or produces different rank orderings of locations.

Figures

Figures reproduced from arXiv: 2604.08374 by Alex Hodge, Melissa Barrientos Trinanes.

**Figure 1.** Figure 1: Delta-compressed CSR encoding. Sorted neighbour indices yield small deltas that fit in one or two LEB128 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: GPU HyperBall execution pipeline. HLL register arrays reside in VRAM throughout. Compressed graph [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Our tool (p = 10, depth limit 3) vs depthmapX for a representative configuration. Mean Depth (left) annotated with Pearson r; Integration [HH] (right) annotated with Spearman ρ. 4.3 Performance and Scaling [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Depth-limited BFS comparison at 11 555 cells (p = 10). (a) Absolute BFS time: depthmapX shows no reduction with decreasing depth, while HyperBall cost scales linearly with iteration count. (b) Speedup relative to each tool’s own unlimited-depth time: our depth-3 BFS is 2.4× faster than our unlimited run, while depthmapX shows negligible benefit from depth limiting. tested depth settings including unlimited… view at source ↗

**Figure 5.** Figure 5: Accuracy across depth limits at 11 555 cells (p = 10, depths 3–unlimited). (a) Mean Depth Pearson r ≥ 0.999 at all depths. (b) Integration [HH] Pearson r remains above 0.97 at all tested depths. 10 2 10 3 10 4 10 5 Grid cells 10 2 10 1 10 0 10 1 10 2 10 3 Visibility construction time (s) (a) Visibility graph construction depthmapX Ours (SparkSieve) SparkSieve 10 2 10 3 10 4 10 5 Grid cells 10 2 10 1 10 0 1… view at source ↗

**Figure 6.** Figure 6: Log-log scaling by grid cells. (a) Visibility graph construction: our SparkSieve implementation compared [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Log-log scaling by graph edges. Plotting time against [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: Speedup of our tool over depthmapX (Tdm/Tours) by area radius and grid spacing, at four HLL precisions. Hatched cells indicate depthmapX timeouts (no reference time available). Values below 1× at coarse spacings reflect GPU initialisation overhead dominating small graphs (see crossover discussion in text). GPU scaling ceiling. The quadratic log-log fits in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 9.** Figure 9: Accuracy heatmaps by area radius and grid spacing. Top row: Pearson [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: Visual Integration [HH] for Valdivia at 5 m spacing with 400 m radius (2.7 × 106 cells, 12.1 × 109 edges). Successive panels zoom from the full 49.45 km2 study area to a 500 m × 500 m street-level detail. Dashed boxes indicate the extent of the next zoom level. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

read the original abstract

Visibility Graph Analysis (VGA) is a key space syntax method for understanding how spatial configuration shapes human movement, but its reliance on all-pairs BFS computation limits practical application to small study areas. We present a system that combines three techniques to scale VGA to city-scale problems: (i) delta-compressed CSR storage using LEB128 varint encoding, which achieves ~4x compression and enables memory-mapped graphs exceeding available RAM; (ii) HyperBall, a probabilistic distance estimator based on HyperLogLog counter propagation, applied here for the first time to visibility graphs, reducing BFS complexity from O(N|E|) to O(D|E|2^p); and (iii) GPU-accelerated CUDA kernels with a fused decode-union kernel that streams the compressed graph via PCIe and performs LEB128 decoding entirely in shared memory. HyperBall's iteration count equals the topological depth limit, so the radius-n analysis that practitioners already use as standard translates directly into proportional speedup -- unlike depthmapX, whose BFS time is invariant to depth setting due to the small diameter of visibility graphs. Using depthmapX's own visibility algorithm (sparkSieve2) to ensure identical edge sets, our tool achieves a 239x end-to-end speedup at 42,705 cells and scales to 236,000 cells (4.8 billion edges) in 137 seconds -- problem sizes far beyond depthmapX's practical limit. At p=10, Visual Mean Depth achieves Pearson r=0.999 with 1.7% median relative error across 20 matched configurations.

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 gets city-scale VGA running in minutes via HyperBall plus GPU compression but only validates the approximation on mean depth.

read the letter

The main point is that this system makes visibility graph analysis practical at city scale by combining LEB128-compressed CSR storage, HyperBall for approximate distances, and a fused CUDA kernel that streams and decodes the graph on the fly. They report a 239x end-to-end speedup versus depthmapX at 42k cells and a full run on 236k cells with 4.8 billion edges in 137 seconds, with the iteration count scaling directly to the chosen depth limit. That is a concrete engineering win over exact all-pairs BFS, which does not benefit from radius limits in the same way. They also match edge sets exactly by reusing depthmapX's visibility step, so the comparison is fair on that axis, and they show Pearson r=0.999 with 1.7% median relative error for Visual Mean Depth at p=10 across 20 configurations. Those numbers are useful to see in print. The work is new in applying HyperBall to visibility graphs at all and in the specific fused kernel design. The scaling result itself is not in the prior literature they cite. The soft spots are limited but real. Accuracy is reported only for mean depth; nothing is shown for visual choice, integration, or other metrics that depend on path counts rather than neighborhood sizes. HyperBall propagates counters for size estimates, so the error behavior for betweenness-style quantities is not automatic and needs checking. There is also no ablation of the three techniques and no error bars on the probabilistic estimator. The assumption that fixed p=10 works across standard VGA metrics therefore rests on one data point. This paper is for space-syntax researchers and urban analysts who already use VGA but are blocked by size. It deserves peer review because the performance claims are grounded in matching baselines and real wall-clock data, even if the validation needs to be broadened before the city-scale claim is fully convincing.

Referee Report

2 major / 2 minor

Summary. The paper introduces a GPU-accelerated system for city-scale Visibility Graph Analysis (VGA) that combines delta-compressed CSR storage via LEB128 encoding, the HyperBall probabilistic distance estimator based on HyperLogLog counter propagation, and custom CUDA kernels with a fused decode-union operation. It claims a 239x end-to-end speedup over depthmapX at 42,705 cells while scaling to 236,000 cells (4.8 billion edges) in 137 seconds, with the HyperBall iteration count directly mapping to standard radius-n analysis; accuracy is reported as Pearson r=0.999 and 1.7% median relative error for Visual Mean Depth at p=10 across 20 matched configurations using identical edge sets from sparkSieve2.

Significance. If the accuracy of the HyperBall approximation extends reliably to the full set of standard VGA metrics, the work would enable practical analysis of urban areas orders of magnitude larger than current tools allow, directly addressing the all-pairs BFS bottleneck in space syntax. The explicit use of matching edge sets from an established baseline and the parameter-free mapping of radius-n to iteration count are notable strengths that support reproducible empirical claims.

major comments (2)

[Experimental evaluation] Experimental evaluation (as summarized in the abstract and results): accuracy is quantified solely for Visual Mean Depth via Pearson correlation and relative error. No corresponding results, error bounds, or comparisons are provided for other core VGA metrics such as visual choice (betweenness) or integration, which aggregate shortest-path counts differently; because the central scaling claim is framed for general VGA applicability, this gap is load-bearing and requires explicit validation or error analysis for those quantities.
[Abstract and methods] Abstract and methods description of HyperBall: the claim that the approach reduces complexity to O(D|E|2^p) and preserves 'usable results for standard VGA' rests on fixed p=10 without reported ablation of the three techniques (compression, HyperBall, GPU kernel) or sensitivity analysis; the absence of such controls leaves unclear how much each component contributes to the reported 239x speedup and 137-second scaling result.

minor comments (2)

[Results] The probabilistic estimator lacks reported error bars or variance estimates across runs, which would strengthen the 1.7% median relative error claim for Visual Mean Depth.
[Implementation] Notation for the fused decode-union kernel and LEB128 streaming could be clarified with a small pseudocode or data-flow diagram to aid readers unfamiliar with the CUDA implementation details.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions. We address each of the major comments in detail below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

Referee: [Experimental evaluation] Experimental evaluation (as summarized in the abstract and results): accuracy is quantified solely for Visual Mean Depth via Pearson correlation and relative error. No corresponding results, error bounds, or comparisons are provided for other core VGA metrics such as visual choice (betweenness) or integration, which aggregate shortest-path counts differently; because the central scaling claim is framed for general VGA applicability, this gap is load-bearing and requires explicit validation or error analysis for those quantities.

Authors: We agree that the evaluation is limited to Visual Mean Depth, which is the metric most directly supported by the HyperBall distance estimation technique. Other metrics like visual choice (betweenness) require not only distances but also the enumeration or sampling of shortest paths, which our current implementation does not provide. To address this, we will revise the manuscript to explicitly state that the validated results are for Visual Mean Depth and discuss the limitations for other metrics. We will also add a note on potential extensions using additional probabilistic methods for path counting if feasible. This clarification will better align the claims with the presented evidence. revision: yes
Referee: [Abstract and methods] Abstract and methods description of HyperBall: the claim that the approach reduces complexity to O(D|E|2^p) and preserves 'usable results for standard VGA' rests on fixed p=10 without reported ablation of the three techniques (compression, HyperBall, GPU kernel) or sensitivity analysis; the absence of such controls leaves unclear how much each component contributes to the reported 239x speedup and 137-second scaling result.

Authors: The complexity reduction to O(D|E|2^p) is a property of the HyperBall algorithm itself, as established in the original HyperBall literature, and is independent of the storage and acceleration techniques. The LEB128 compression and GPU kernels are engineering contributions that enable the practical application at scale. While we did not include a full ablation study in the original submission, we can provide additional analysis in the revision: for instance, we can report the performance with and without compression (noting the ~4x memory reduction), and compare GPU vs CPU implementations where possible. For p, we chose p=10 based on prior work for the accuracy-speed tradeoff, and we will add a sensitivity plot showing accuracy vs p for Visual Mean Depth. This will clarify the contributions without altering the core results. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation or validation chain

full rationale

The paper implements HyperBall (an external probabilistic estimator based on HyperLogLog) on visibility graphs produced by an independent algorithm (sparkSieve2 from depthmapX), then measures end-to-end speedup and Pearson correlation for Visual Mean Depth against that exact baseline on matched edge sets. No target metric is defined in terms of the approximation itself, no parameters are fitted to the reported results, and no self-citations or uniqueness theorems are invoked to justify the core claims. The reported 239x speedup and r=0.999 correlation are direct empirical measurements on real data rather than reductions to fitted inputs or prior self-work. The limitation that only mean depth (not betweenness or integration) is validated is a scope issue, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central performance claim rests on standard properties of HyperLogLog cardinality estimation and CSR graph representation; the only tunable element is the HyperLogLog precision parameter.

free parameters (1)

p = 10
HyperLogLog register count that trades memory for estimation accuracy; set to 10 to achieve the reported 1.7% median error.

axioms (2)

standard math HyperLogLog counters yield unbiased cardinality estimates whose relative error decreases with register count p.
Invoked when stating that iteration count equals topological depth and that p=10 suffices for VGA metrics.
standard math LEB128 varint encoding is lossless for the delta-compressed CSR adjacency lists.
Required for the claim that memory-mapped graphs exceed RAM without altering edge sets.

pith-pipeline@v0.9.0 · 5582 in / 1409 out tokens · 65609 ms · 2026-05-10T16:53:44.891725+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

HyperBall ... reducing BFS complexity from O(N|E|) to O(D|E|2^p); ... Visual Mean Depth achieves Pearson r=0.999
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

delta-compressed CSR storage using LEB128 varint encoding ... GPU-accelerated CUDA kernels

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

[1]

Cambridge University Press, Cambridge, 1996

Bill Hillier.Space is the Machine: A Configurational Theory of Architecture. Cambridge University Press, Cambridge, 1996

work page 1996
[2]

Cambridge University Press, Cambridge, 1984

Bill Hillier and Julienne Hanson.The Social Logic of Space. Cambridge University Press, Cambridge, 1984

work page 1984
[3]

From isovists to visibility graphs: a methodol- ogy for the analysis of architectural space.Environment and Planning B: Planning and Design, 28(1):103–121, 2001

Alasdair Turner, Maria Doxa, David O’Sullivan, and Alan Penn. From isovists to visibility graphs: a methodol- ogy for the analysis of architectural space.Environment and Planning B: Planning and Design, 28(1):103–121, 2001

work page 2001
[4]

depthmapX: Multi-platform spatial network analysis software.https://github.com/ SpaceGroupUCL/depthmapX, 2012

Tasos Varoudis. depthmapX: Multi-platform spatial network analysis software.https://github.com/ SpaceGroupUCL/depthmapX, 2012. Open-source implementation of space syntax methods

work page 2012
[5]

In-core computation of geometric centralities with HyperBall: A hundred billion nodes and beyond

Paolo Boldi and Sebastiano Vigna. In-core computation of geometric centralities with HyperBall: A hundred billion nodes and beyond. InProceedings of the IEEE 13th International Conference on Data Mining Workshops (ICDMW), pages 784–791. IEEE, 2013

work page 2013
[6]

Depthmap 4: A researcher’s handbook

Alasdair Turner. Depthmap 4: A researcher’s handbook. Technical report, Bartlett School of Graduate Studies, University College London, London, 2004

work page 2004
[7]

Dissecting visibility graph analysis: the metrics and their role in understanding workplace human behaviour

Petros Koutsolampros, Kerstin Sailer, Tasos Varoudis, and Rosie Haslem. Dissecting visibility graph analysis: the metrics and their role in understanding workplace human behaviour. InProceedings of the 12th International Space Syntax Symposium, pages 191:1–191:24, Beijing, China, 2019

work page 2019
[8]

To take hold of space: Isovists and isovist fields.Environment and Planning B: Planning and Design, 6(1):47–65, 1979

Michael L Benedikt. To take hold of space: Isovists and isovist fields.Environment and Planning B: Planning and Design, 6(1):47–65, 1979

work page 1979
[9]

Space syntax standardised integration measures and some simulations.Environment and Planning B: Planning and Design, 20(3):347–357, 1993

Jan AF Teklenburg, Harry JP Timmermans, and Anton F van Wagenberg. Space syntax standardised integration measures and some simulations.Environment and Planning B: Planning and Design, 20(3):347–357, 1993. 14 City-Scale Visibility Graph Analysis via GPU-Accelerated HyperBallA PREPRINT

work page 1993
[10]

Collective dynamics of ‘small-world’ networks.Nature, 393(6684):440– 442, 1998

Duncan J Watts and Steven H Strogatz. Collective dynamics of ‘small-world’ networks.Nature, 393(6684):440– 442, 1998

work page 1998
[11]

Analysis of the effects of urban form on neighborhood vitality: five cases in Valdivia, Southern Chile.Journal of Housing and the Built Environment, 34:897–925, 2019

Antonio Zumelzu and Melissa Barrientos-Trinanes. Analysis of the effects of urban form on neighborhood vitality: five cases in Valdivia, Southern Chile.Journal of Housing and the Built Environment, 34:897–925, 2019

work page 2019
[12]

Viraph: exploring the potentials of visibility graphs and their analysis.Visualization in Engineering, 5(17), 2017

Peiman Amini Behbahani, Ning Gu, and Michael Ostwald. Viraph: exploring the potentials of visibility graphs and their analysis.Visualization in Engineering, 5(17), 2017. Open Access

work page 2017
[13]

Fast approximation of centrality.Journal of Graph Algorithms and Applica- tions, 8(1):39–45, 2004

David Eppstein and Joseph Wang. Fast approximation of centrality.Journal of Graph Algorithms and Applica- tions, 8(1):39–45, 2004

work page 2004
[14]

Fast shortest path distance estima- tion in large networks

Michalis Potamias, Francesco Bonchi, Carlos Castillo, and Aristides Gionis. Fast shortest path distance estima- tion in large networks. InProceedings of the 18th ACM Conference on Information and Knowledge Management, pages 867–876, 2009

work page 2009
[15]

HyperLogLog: the analysis of a near- optimal cardinality estimation algorithm.Discrete Mathematics and Theoretical Computer Science, AH:137– 156, 2007

Philippe Flajolet, Éric Fusy, Olivier Gandouet, and Frédéric Meunier. HyperLogLog: the analysis of a near- optimal cardinality estimation algorithm.Discrete Mathematics and Theoretical Computer Science, AH:137– 156, 2007

work page 2007
[16]

HyperANF: Approximating the neighbourhood function of very large graphs on a budget

Paolo Boldi, Marco Rosa, and Sebastiano Vigna. HyperANF: Approximating the neighbourhood function of very large graphs on a budget. InProceedings of the 20th International Conference on World Wide Web, pages 625–634, 2011

work page 2011
[17]

Rayon: A data parallelism library for Rust.https://github.com/rayon-rs/rayon,

Rayon Contributors. Rayon: A data parallelism library for Rust.https://github.com/rayon-rs/rayon,

work page
[18]

Natural movement: Or, configuration and attraction in urban pedestrian movement.Environment and Planning B: Planning and Design, 20(1):29–66, 1993

Bill Hillier, Alan Penn, Julienne Hanson, Tadeusz Grajewski, and Jin Xu. Natural movement: Or, configuration and attraction in urban pedestrian movement.Environment and Planning B: Planning and Design, 20(1):29–66, 1993

work page 1993
[19]

edge effects

Jorge Gil. Street network analysis “edge effects”: Examining the sensitivity of centrality measures to boundary conditions.Environment and Planning B: Urban Analytics and City Science, 44(5):819–836, 2017

work page 2017
[20]

John David Ericson, Elizabeth R Chrastil, and William H Warren. On the robustness of visibility graph analysis in the built environment: Repeat measures, boundary effects, and the impact of grid resolution.Environment and Planning B: Urban Analytics and City Science, 48(4):879–896, 2021

work page 2021
[21]

The space syntax toolkit: Integrating depthmapX and exploratory spatial analysis workflows in QGIS

Jorge Gil, Tasos Varoudis, Kayvan Karimi, and Alan Penn. The space syntax toolkit: Integrating depthmapX and exploratory spatial analysis workflows in QGIS. InProceedings of the 10th International Space Syntax Symposium (SSS10), pages 148:1–148:12, London, UK, 2015. Space Syntax Laboratory, The Bartlett, UCL. 15 City-Scale Visibility Graph Analysis via GP...

work page 2015

[1] [1]

Cambridge University Press, Cambridge, 1996

Bill Hillier.Space is the Machine: A Configurational Theory of Architecture. Cambridge University Press, Cambridge, 1996

work page 1996

[2] [2]

Cambridge University Press, Cambridge, 1984

Bill Hillier and Julienne Hanson.The Social Logic of Space. Cambridge University Press, Cambridge, 1984

work page 1984

[3] [3]

From isovists to visibility graphs: a methodol- ogy for the analysis of architectural space.Environment and Planning B: Planning and Design, 28(1):103–121, 2001

Alasdair Turner, Maria Doxa, David O’Sullivan, and Alan Penn. From isovists to visibility graphs: a methodol- ogy for the analysis of architectural space.Environment and Planning B: Planning and Design, 28(1):103–121, 2001

work page 2001

[4] [4]

depthmapX: Multi-platform spatial network analysis software.https://github.com/ SpaceGroupUCL/depthmapX, 2012

Tasos Varoudis. depthmapX: Multi-platform spatial network analysis software.https://github.com/ SpaceGroupUCL/depthmapX, 2012. Open-source implementation of space syntax methods

work page 2012

[5] [5]

In-core computation of geometric centralities with HyperBall: A hundred billion nodes and beyond

Paolo Boldi and Sebastiano Vigna. In-core computation of geometric centralities with HyperBall: A hundred billion nodes and beyond. InProceedings of the IEEE 13th International Conference on Data Mining Workshops (ICDMW), pages 784–791. IEEE, 2013

work page 2013

[6] [6]

Depthmap 4: A researcher’s handbook

Alasdair Turner. Depthmap 4: A researcher’s handbook. Technical report, Bartlett School of Graduate Studies, University College London, London, 2004

work page 2004

[7] [7]

Dissecting visibility graph analysis: the metrics and their role in understanding workplace human behaviour

Petros Koutsolampros, Kerstin Sailer, Tasos Varoudis, and Rosie Haslem. Dissecting visibility graph analysis: the metrics and their role in understanding workplace human behaviour. InProceedings of the 12th International Space Syntax Symposium, pages 191:1–191:24, Beijing, China, 2019

work page 2019

[8] [8]

To take hold of space: Isovists and isovist fields.Environment and Planning B: Planning and Design, 6(1):47–65, 1979

Michael L Benedikt. To take hold of space: Isovists and isovist fields.Environment and Planning B: Planning and Design, 6(1):47–65, 1979

work page 1979

[9] [9]

Space syntax standardised integration measures and some simulations.Environment and Planning B: Planning and Design, 20(3):347–357, 1993

Jan AF Teklenburg, Harry JP Timmermans, and Anton F van Wagenberg. Space syntax standardised integration measures and some simulations.Environment and Planning B: Planning and Design, 20(3):347–357, 1993. 14 City-Scale Visibility Graph Analysis via GPU-Accelerated HyperBallA PREPRINT

work page 1993

[10] [10]

Collective dynamics of ‘small-world’ networks.Nature, 393(6684):440– 442, 1998

Duncan J Watts and Steven H Strogatz. Collective dynamics of ‘small-world’ networks.Nature, 393(6684):440– 442, 1998

work page 1998

[11] [11]

Analysis of the effects of urban form on neighborhood vitality: five cases in Valdivia, Southern Chile.Journal of Housing and the Built Environment, 34:897–925, 2019

Antonio Zumelzu and Melissa Barrientos-Trinanes. Analysis of the effects of urban form on neighborhood vitality: five cases in Valdivia, Southern Chile.Journal of Housing and the Built Environment, 34:897–925, 2019

work page 2019

[12] [12]

Viraph: exploring the potentials of visibility graphs and their analysis.Visualization in Engineering, 5(17), 2017

Peiman Amini Behbahani, Ning Gu, and Michael Ostwald. Viraph: exploring the potentials of visibility graphs and their analysis.Visualization in Engineering, 5(17), 2017. Open Access

work page 2017

[13] [13]

Fast approximation of centrality.Journal of Graph Algorithms and Applica- tions, 8(1):39–45, 2004

David Eppstein and Joseph Wang. Fast approximation of centrality.Journal of Graph Algorithms and Applica- tions, 8(1):39–45, 2004

work page 2004

[14] [14]

Fast shortest path distance estima- tion in large networks

Michalis Potamias, Francesco Bonchi, Carlos Castillo, and Aristides Gionis. Fast shortest path distance estima- tion in large networks. InProceedings of the 18th ACM Conference on Information and Knowledge Management, pages 867–876, 2009

work page 2009

[15] [15]

HyperLogLog: the analysis of a near- optimal cardinality estimation algorithm.Discrete Mathematics and Theoretical Computer Science, AH:137– 156, 2007

Philippe Flajolet, Éric Fusy, Olivier Gandouet, and Frédéric Meunier. HyperLogLog: the analysis of a near- optimal cardinality estimation algorithm.Discrete Mathematics and Theoretical Computer Science, AH:137– 156, 2007

work page 2007

[16] [16]

HyperANF: Approximating the neighbourhood function of very large graphs on a budget

Paolo Boldi, Marco Rosa, and Sebastiano Vigna. HyperANF: Approximating the neighbourhood function of very large graphs on a budget. InProceedings of the 20th International Conference on World Wide Web, pages 625–634, 2011

work page 2011

[17] [17]

Rayon: A data parallelism library for Rust.https://github.com/rayon-rs/rayon,

Rayon Contributors. Rayon: A data parallelism library for Rust.https://github.com/rayon-rs/rayon,

work page

[18] [18]

Natural movement: Or, configuration and attraction in urban pedestrian movement.Environment and Planning B: Planning and Design, 20(1):29–66, 1993

Bill Hillier, Alan Penn, Julienne Hanson, Tadeusz Grajewski, and Jin Xu. Natural movement: Or, configuration and attraction in urban pedestrian movement.Environment and Planning B: Planning and Design, 20(1):29–66, 1993

work page 1993

[19] [19]

edge effects

Jorge Gil. Street network analysis “edge effects”: Examining the sensitivity of centrality measures to boundary conditions.Environment and Planning B: Urban Analytics and City Science, 44(5):819–836, 2017

work page 2017

[20] [20]

John David Ericson, Elizabeth R Chrastil, and William H Warren. On the robustness of visibility graph analysis in the built environment: Repeat measures, boundary effects, and the impact of grid resolution.Environment and Planning B: Urban Analytics and City Science, 48(4):879–896, 2021

work page 2021

[21] [21]

The space syntax toolkit: Integrating depthmapX and exploratory spatial analysis workflows in QGIS

Jorge Gil, Tasos Varoudis, Kayvan Karimi, and Alan Penn. The space syntax toolkit: Integrating depthmapX and exploratory spatial analysis workflows in QGIS. InProceedings of the 10th International Space Syntax Symposium (SSS10), pages 148:1–148:12, London, UK, 2015. Space Syntax Laboratory, The Bartlett, UCL. 15 City-Scale Visibility Graph Analysis via GP...

work page 2015