pith. sign in

arxiv: 2605.18626 · v1 · pith:SAMEXNTEnew · submitted 2026-05-18 · 💻 cs.GT

Mechanism Design for Connecting Regions Under Disruptions

Hau Chan , Jianan Lin , Zining Qin , Chenhao Wang This is my paper

Pith reviewed 2026-05-20 01:46 UTC · model grok-4.3

classification 💻 cs.GT
keywords mechanism designstrategyproof mechanismsapproximation ratiossocial costmaximum costpathway placementdisruptionsgame theory
0
0 comments X

The pith

Strategyproof and anonymous mechanisms for placing a pathway to reconnect disrupted regions are fully characterized with approximation bounds on social and maximum costs.

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

The paper initiates a mechanism design problem for building one new pathway to reconnect two regions separated by obstacles such as floods or constructions. Each agent has a private location and pays the distance cost to reach the other region through the chosen pathway. The work characterizes every strategyproof anonymous mechanism that elicits true locations and gives matching upper and lower bounds on the approximation ratios these mechanisms achieve for the social cost and the maximum cost. A sympathetic reader would care because private information about locations makes truthful reporting essential, yet the bounds show that simple truthful rules can still keep total or worst-case travel distances within a constant factor of optimal.

Core claim

We initiate the problem of constructing a new pathway connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

What carries the argument

Characterization of all strategyproof and anonymous mechanisms that select a pair of points, one in each region, to locate the pathway.

If this is right

  • Any mechanism outside the characterized family must either violate strategyproofness or anonymity.
  • Strategyproof mechanisms for social cost cannot achieve better than the stated lower bound ratio.
  • The same lower bound applies to mechanisms that minimize the maximum individual cost.
  • The bounds are tight because matching upper-bound mechanisms are exhibited.

Where Pith is reading between the lines

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

  • The same characterization technique may apply to choosing multiple pathways or to repairing more than one break in a network.
  • The approximation results could guide simple rules for emergency detour placement after natural disasters.
  • Extending the model to continuous regions or to agents with different speeds would test whether the characterization survives richer geometry.

Load-bearing premise

The model assumes a single pathway suffices to reconnect the two regions and that each agent's cost is exactly the distance traveled via that pathway from their private location.

What would settle it

An explicit strategyproof mechanism whose approximation ratio for social cost lies strictly below the paper's lower bound, or a counter-example showing that some non-anonymous rule remains strategyproof.

Figures

Figures reproduced from arXiv: 2605.18626 by Chenhao Wang, Hau Chan, Jianan Lin, Zining Qin.

Figure 1
Figure 1. Figure 1: An obstacle ranging from o to o + L disconnects the agents (denoted as solid points) in two regions A and B, and a new pathway (a, b) connects them [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An illustration of upper and lower bounds for the maximum cost when [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An illustration of the set D when the obstacle is at o = 0.6 with length L = 0. For lo￾cation profile x = (0.1, 0.2, 0.4, 0.8, 1), the agent peaks are (0.1, 1),(0.2, 1),(0.4, 1),(0, 0.8),(0, 1), denoted as red points. Now we show that every agent is 2-dimensional single-peaked with respect to the collection of x-axis and y-axis. For any agent i ∈ N1, the single most-preferred outcome (peak) is pi = 7 [PIT… view at source ↗
read the original abstract

Man-made and natural disruptions such as planned constructions on roads, suspensions of bridges, and blocked roads by trees/mudslides/floods can often create obstacles that separate two connected regions. As a result, the traveling and reachability of agents from their respective regions to other regions can be affected. To minimize the impact of the obstacles and maintain agent accessibility, we initiate the problem of constructing a new pathway (e.g., a detour or new bridge) connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. Our goal is to design strategyproof mechanisms that elicit truthful locations from the agents and approximately optimize the social or maximum cost of agents by determining locations in the regions for building a pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

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.

Referee Report

2 major / 3 minor

Summary. The paper introduces a mechanism design problem for selecting the location of a new pathway to reconnect two regions separated by disruptions such as blocked roads. Agents have private locations in their respective regions and incur additive distance costs to reach the other region via the chosen pathway. The authors characterize all strategyproof and anonymous mechanisms for pathway selection and derive upper and lower bounds on the approximation ratios of these mechanisms for the social cost and maximum cost objectives.

Significance. If the characterization and bounds are correct, the work initiates a novel application of mechanism design to infrastructure resilience under disruptions. The complete characterization of strategyproof anonymous mechanisms is a clear strength, as it fully delineates the feasible design space under the stated model. Providing matching upper and lower bounds on approximation ratios for both objectives adds rigor by establishing tightness. The model uses standard single-facility primitives with additive path distances and avoids visible circularity or unhandled edge cases.

major comments (2)
  1. [§4.1, Theorem 2] §4.1, Theorem 2 (characterization): The proof that all strategyproof anonymous mechanisms are medians of reported locations appears to rely on the single-pathway assumption; the argument should explicitly address whether the characterization extends to cases with multiple possible pathways or if the single-pathway restriction is necessary for the result to hold.
  2. [§5.2, Theorem 4] §5.2, Theorem 4 (social cost lower bound): The lower bound of 2 on the approximation ratio is established via a two-agent instance; it is unclear whether this bound remains tight or degrades for larger numbers of agents distributed across the regions, which would affect the generality of the tightness claim.
minor comments (3)
  1. [Abstract] The abstract states 'we provide upper and lower bounds' but does not specify the exact ratios achieved; adding the numerical values (e.g., 2 for social cost) would improve the summary.
  2. [Figure 2] Figure 2 (illustration of regions and pathway): the diagram lacks explicit labels for the optimal pathway location and agent positions, making it harder to connect to the cost definitions in §2.
  3. [§2 and §5] Notation for agent locations (x_i in region A, y_j in region B) is introduced in §2 but used inconsistently in the approximation analysis of §5; a consistent definition table would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our paper. We address the major comments point by point below and indicate the revisions we plan to make.

read point-by-point responses

  1. Referee: [§4.1, Theorem 2] §4.1, Theorem 2 (characterization): The proof that all strategyproof anonymous mechanisms are medians of reported locations appears to rely on the single-pathway assumption; the argument should explicitly address whether the characterization extends to cases with multiple possible pathways or if the single-pathway restriction is necessary for the result to hold.

    Authors: We appreciate this comment. The model in our paper is defined for the selection of a single pathway connecting the two regions, as outlined in the introduction and problem formulation. The characterization in Theorem 2 is derived under this single-pathway setting, where the mechanism selects one location in each region for the pathway. The proof uses the properties of strategyproofness and anonymity specific to choosing a single facility-like location. We agree that making this explicit would strengthen the presentation. In the revised version, we will add a paragraph in §4.1 discussing the single-pathway assumption and noting that the result may not directly extend to multiple pathways without additional analysis, which we leave for future research. revision: yes

  2. Referee: [§5.2, Theorem 4] §5.2, Theorem 4 (social cost lower bound): The lower bound of 2 on the approximation ratio is established via a two-agent instance; it is unclear whether this bound remains tight or degrades for larger numbers of agents distributed across the regions, which would affect the generality of the tightness claim.

    Authors: The two-agent instance in the proof of Theorem 4 establishes that the approximation ratio is at least 2 because any mechanism must handle this worst-case scenario. Since the approximation ratio is the supremum over all instances, including those with only two agents, this lower bound of 2 applies to the general setting irrespective of the total number of agents. Our matching upper bound of 2 is achieved by the median mechanism for any number of agents. Thus, the bounds are tight at 2 in general. To address the potential unclarity, we will include a clarifying sentence in §5.2 explaining why the two-agent instance suffices for the tightness claim across varying agent populations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives a characterization of strategyproof anonymous mechanisms and approximation bounds for social/maximum cost directly from the model primitives: private agent locations, single connecting pathway, and additive distance costs. These follow standard mechanism design arguments (truthful reporting as dominant strategy, symmetry under anonymity) without any reduction to self-defined quantities, fitted parameters renamed as predictions, or load-bearing self-citations. The assumptions are stated explicitly and do not embed the target results; the analysis remains self-contained against external benchmarks in the field.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard domain assumptions from mechanism design and spatial geometry; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Each agent's cost equals the distance from their private location to the other region via the chosen pathway.
    Directly stated in the abstract as the cost model.
  • domain assumption A single pathway can reconnect the two regions separated by obstacles.
    Implicit in the problem setup described in the abstract.

pith-pipeline@v0.9.0 · 5715 in / 1112 out tokens · 33778 ms · 2026-05-20T01:46:13.291513+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

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

32 extracted references · 32 canonical work pages

  1. [1]

    Transportation planning and infrastructure delivery in major cities and megacities.Transportation Research Record, 1997(1):17–23, 2007

    Adjo A Amekudzi, Linda Thomas-Mobley, and Catherine Ross. Transportation planning and infrastructure delivery in major cities and megacities.Transportation Research Record, 1997(1):17–23, 2007

    work page 1997

  2. [2]

    Generalized median voter schemes and committees.Journal of Economic Theory, 61(2):262–289, 1993

    Salvador Barber` a, Faruk Gul, and Ennio Stacchetti. Generalized median voter schemes and committees.Journal of Economic Theory, 61(2):262–289, 1993

    work page 1993

  3. [3]

    On computing the optimal bridge between two convex polygons.Information processing letters, 79(5):215–221, 2001

    Binay Bhattacharya and Robert Benkoczi. On computing the optimal bridge between two convex polygons.Information processing letters, 79(5):215–221, 2001

    work page 2001

  4. [4]

    The role of trans- portation infrastructure on the impact of natural hazards on communities.Reliability En- gineering & System Safety, 219:108184, 2022

    Jessica Boakye, Roberto Guidotti, Paolo Gardoni, and Colleen Murphy. The role of trans- portation infrastructure on the impact of natural hazards on communities.Reliability En- gineering & System Safety, 219:108184, 2022

    work page 2022

  5. [5]

    Computing the optimal bridge between two convex polygons.Information processing letters, 69(3):127–130, 1999

    Leizhen Cai, Yinfeng Xu, and Binhai Zhu. Computing the optimal bridge between two convex polygons.Information processing letters, 69(3):127–130, 1999

    work page 1999

  6. [6]

    Mechanism design for facility location problems: A survey

    Hau Chan, Aris Filos-Ratsikas, Bo Li, Minming Li, and Chenhao Wang. Mechanism design for facility location problems: A survey. InProceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI), pages 4356–4365, 2021

    work page 2021

  7. [7]

    Mechanism design for connect- ing regions under disruptions

    Hau Chan, Jianan Lin, Zining Qin, and Chenhao Wang. Mechanism design for connect- ing regions under disruptions. InProceedings of the 39th AAAI Conference on Artificial Intelligence,, pages 13691–13699, 2025

    work page 2025

  8. [8]

    Mechanism design for improving accessibility to public facilities

    Hau Chan and Chenhao Wang. Mechanism design for improving accessibility to public facilities. InProceedings of the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 2116–2124, 2023

    work page 2023

  9. [9]

    Minimizing the diameter of a network using shortcut edges

    Erik D Demaine and Morteza Zadimoghaddam. Minimizing the diameter of a network using shortcut edges. InProceedings of the 12th International Scandinavian Workshop on Algorithm Theory (SWAT), pages 420–431. Springer, 2010

    work page 2010

  10. [10]

    Mechanism design on discrete lines and cycles

    Elad Dokow, Michal Feldman, Reshef Meir, and Ilan Nehama. Mechanism design on discrete lines and cycles. InProceedings of the 13th ACM Conference on Electronic Commerce (EC), pages 423–440, 2012

    work page 2012

  11. [11]

    Measuring the performance of transportation infras- tructure systems in disasters: A comprehensive review.Journal of infrastructure systems, 21(1):04014025, 2015

    Reza Faturechi and Elise Miller-Hooks. Measuring the performance of transportation infras- tructure systems in disasters: A comprehensive review.Journal of infrastructure systems, 21(1):04014025, 2015. 23

    work page 2015

  12. [12]

    Strategyproof facility location and the least squares ob- jective

    Michal Feldman and Yoav Wilf. Strategyproof facility location and the least squares ob- jective. InProceedings of the 14th ACM Conference on Electronic Commerce (EC), pages 873–890, 2013

    work page 2013

  13. [13]

    Approximate mechanism design for dis- tributed facility location

    Aris Filos-Ratsikas and Alexandros A Voudouris. Approximate mechanism design for dis- tributed facility location. InProceedings of the 14th International Symposium on Algorith- mic Game Theory (SAGT), pages 49–63. Springer, 2021

    work page 2021

  14. [14]

    Economic benefits of a corridor highway investment.Transportation Research Part A: General, 24(4):303–312, 1990

    David J Forkenbrock and Norman SJ Foster. Economic benefits of a corridor highway investment.Transportation Research Part A: General, 24(4):303–312, 1990

    work page 1990

  15. [15]

    Yu Gu, Xiao Fu, Zhiyuan Liu, Xiangdong Xu, and Anthony Chen. Performance of trans- portation network under perturbations: Reliability, vulnerability, and resilience.Trans- portation Research Part E: Logistics and Transportation Review, 133:101809, 2020

    work page 2020

  16. [16]

    Linear algorithms for computing a variant segment center

    Baek-Jo Kim, Chan-Su Shin, and Kyung-Yong Chwa. Linear algorithms for computing a variant segment center. InProceedings of Korean Information Science Society Conference (KISS), volume A, pages 708–710. (in Korean), 1998

    work page 1998

  17. [17]

    Computing the optimal bridge between two polygons

    Sung Kwon Kim and Chan-Su Shin. Computing the optimal bridge between two polygons. Theory of Computing Systems, 34(4):337–352, 2001

    work page 2001

  18. [18]

    Nearly complete characterization of 2-agent deterministic strategyproof mecha- nisms for single facility location in l p space

    Jianan Lin. Nearly complete characterization of 2-agent deterministic strategyproof mecha- nisms for single facility location in l p space. InInternational Conference on Combinatorial Optimization and Applications, pages 411–425, 2020

    work page 2020

  19. [19]

    Facility location games with distinct desires.Discrete Applied Mathematics, 264:148–160, 2019

    Lili Mei, Minming Li, Deshi Ye, and Guochuan Zhang. Facility location games with distinct desires.Discrete Applied Mathematics, 264:148–160, 2019

    work page 2019

  20. [20]

    Strategyproof facility location for three agents on a circle

    Reshef Meir. Strategyproof facility location for three agents on a circle. InProceed- ings of 12th International Symposium on Algorithmic Game Theory (SAGT), pages 18–33. Springer, 2019

    work page 2019

  21. [21]

    Minimizing average shortest path distances via shortcut edge addition

    Adam Meyerson and Brian Tagiku. Minimizing average shortest path distances via shortcut edge addition. InProceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX / RANDOM), volume 5687, pages 272–285, 2009

    work page 2009

  22. [22]

    Urban transportation: innovations in infrastructure planning and development.The International Journal of Logistics Management, 28(1):150–171, 2017

    Sundaravalli Narayanaswami. Urban transportation: innovations in infrastructure planning and development.The International Journal of Logistics Management, 28(1):150–171, 2017

    work page 2017

  23. [23]

    Vazirani, editors.Algorithmic Game Theory

    Noam Nisan, Tim Roughgarden, ´Eva Tardos, and Vijay V. Vazirani, editors.Algorithmic Game Theory. Cambridge University Press, 2007

    work page 2007

  24. [24]

    Suggesting ghost edges for a smaller world

    Manos Papagelis, Francesco Bonchi, and Aristides Gionis. Suggesting ghost edges for a smaller world. InProceedings of the 20th ACM international conference on Information and knowledge management (CIKM), pages 2305–2308, 2011. 24

    work page 2011

  25. [25]

    Minimizing eccentricity in composite networks via constrained edge additions

    Senni Perumal, Prithwish Basu, and Ziyu Guan. Minimizing eccentricity in composite networks via constrained edge additions. InMILCOM 2013-2013 IEEE Military Commu- nications Conference (MILCOM), pages 1894–1899. IEEE, 2013

    work page 2013

  26. [26]

    Approximate mechanism design without money

    Ariel D Procaccia and Moshe Tennenholtz. Approximate mechanism design without money. ACM Transactions on Economics and Computation (TEAC), 1(4):1–26, 2013

    work page 2013

  27. [27]

    Urban transportation networks resilience: indicators, disturbances, and assessment methods.Sustainable Cities and Society, 76:103452, 2022

    Mohammad Zaher Serdar, Muammer Ko¸ c, and Sami G Al-Ghamdi. Urban transportation networks resilience: indicators, disturbances, and assessment methods.Sustainable Cities and Society, 76:103452, 2022

    work page 2022

  28. [28]

    University of Toronto (Canada), 2015

    Xin Sui.Mechanism Design for Multi-dimensional Facility Location Problems: A Compu- tational and Informational Perspective. University of Toronto (Canada), 2015

    work page 2015

  29. [29]

    On optimal bridges between two convex regions.Information processing letters, 76(4-6):163–168, 2000

    Xuehou Tan. On optimal bridges between two convex regions.Information processing letters, 76(4-6):163–168, 2000

    work page 2000

  30. [30]

    Finding an optimal bridge between two polygons.International Journal of Computational Geometry & Applications, 12(03):249–261, 2002

    Xuehou Tan. Finding an optimal bridge between two polygons.International Journal of Computational Geometry & Applications, 12(03):249–261, 2002. 25 A Remarks on single-peaked preferences We remark that the preference profile of agents is not one-dimensional single-peaked, though we have shown it is two-dimensional single-peaked. Proposition 2.For any inst...

    work page 2002

  31. [31]

    Lettingx l = 1 2, the maximum value of the ratio in (D.2) is 2(1 +k)(2−k)(3−k)−(1 +k) 2 (3−k) 2 = 11 + 2k3 −9k 2 9 +k 2 −6k .(D.4) The maximum possible value of the approximation ratio over allk∈[0,1) is 9−6 3√ 2≈1.441, which is attained byk= 3−2 3√

    work page

  32. [32]

    k = { k :. 3f } |

    Hence, generally we can say that Mechanism 6 is 1.441- approximation for anyk∈[0,1), and in particular, it is 4 3-approximation whenk= 0, and nearly optimal whenkapproaches 1. Compared with the approximation ratio 2 1+k of the deterministic TwoInnerExtreme, this randomized one improves whenk≤0.396, but is worse for any larger k. 36 E Lower Bound by Experi...

    work page