Scalable Algorithms with Provable Optimality Bounds for the Multiple Watchman Route Problem

Ariel Felner; Jiaoyang Li; Srikar Gouru

arxiv: 2604.15610 · v1 · submitted 2026-04-17 · 💻 cs.MA

Scalable Algorithms with Provable Optimality Bounds for the Multiple Watchman Route Problem

Srikar Gouru , Ariel Felner , Jiaoyang Li This is my paper

Pith reviewed 2026-05-10 08:14 UTC · model grok-4.3

classification 💻 cs.MA

keywords multiple watchman route problemMWRP-CP3state space pruningmulti-agent path planningoptimal planningsuboptimal algorithmsvisibility coverage

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The pith

Pruning methods and the MWRP-CP3 planner reduce the search space for multiple watchman routes by more than 95 percent and run over 200 times faster than prior optimal algorithms on 2D grid maps.

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

The paper addresses the multiple watchman route problem of finding paths for several watchmen so that every point on a map is visible to at least one of them. It proposes pruning techniques to shrink the state space by removing areas that will be seen anyway when traveling to other locations. These prunings are integrated into MWRP-CP3, an optimal algorithm enhanced with better heuristics for faster computation. Suboptimal algorithms are also developed that come with guarantees on how close their solutions are to optimal and can handle much bigger maps. On 2D grid maps the optimal method cuts the search space by more than 95 percent and runs more than 200 times faster than previous optimal solvers.

Core claim

MWRP-CP3 combines pruning of guaranteed-to-be-seen areas with refined heuristics to compute optimal watchman routes with over 95 percent search space reduction and more than 200 times speedup compared to prior optimal algorithms on 2D grids. The suboptimal algorithms including MxWA* provide provable quality bounds and solve instances three times larger than those feasible for the optimal planner.

What carries the argument

Pruning methods that eliminate map areas guaranteed to be seen en route to other areas, used within the MWRP-CP3 planner along with heuristic improvements.

If this is right

Optimal solutions become feasible for maps previously too large for prior optimal methods.
Suboptimal algorithms with provable quality bounds can address instances three times larger.
Anytime variants and decomposition into sub-problems allow iterative improvement of solutions.

Where Pith is reading between the lines

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

The pruning techniques may be tested on maps with varied obstacle layouts to check whether the search-space reduction remains above 95 percent.
The combination of optimal and suboptimal methods could be extended to produce hybrid solvers that trade solution quality for scalability in related coverage tasks.
The decomposition approach for refining solutions might apply to other multi-agent makespan problems if similar visibility guarantees hold.

Load-bearing premise

The pruning methods assume that certain map areas are guaranteed to be seen en route to other areas under the chosen visibility model on the tested 2D grid maps.

What would settle it

A small 2D grid map instance with a known optimal solution cost where MWRP-CP3 after pruning returns a different cost or fails to cover the map.

Figures

Figures reproduced from arXiv: 2604.15610 by Ariel Felner, Jiaoyang Li, Srikar Gouru.

**Figure 2.** Figure 2: Figures(a) and (b) show the watchers (yellow) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of state space reduction showing cells [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Figure 5: Two example search nodes, each with the agent [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 4.** Figure 4: Examples where pivot pruning improves (top) and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: Visualization of the initial joint-space solution, de [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: From left to right, Den101d, Lak105d, Den202d [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: Runtime comparison of search algorithms with respect to map size (top) and agent counts (bottom). Suboptimal [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: Figure(a) shows runtime (lines) and solution cost [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

read the original abstract

In this paper, we tackle the Multiple Watchman Route Problem (MWRP), which aims to find a set of paths that M watchmen can follow such that every location on the map can be seen by at least one watchman. First, we propose multiple methods to reduce the state space over which a search needs to be conducted by pruning map areas that are guaranteed to be seen en route to other areas. Next, we introduce MWRP-CP3, an efficient optimal planner that combines these methods with techniques that improve the quality and calculation time of existing heuristics. We present several suboptimal algorithms with bounds on solution quality, including MxWA*, a general variant of weighted A* for makespan problems. We also present anytime variations of our suboptimal algorithms, as well as techniques to improve an existing suboptimal solution by solving multiple decomposed sub-problems. We show that MWRP-CP3 can reduce the search space by more than 95% and runs more than 200x faster than existing optimal algorithms on 2D grid maps. We also show that our suboptimal algorithms solve maps 3x larger than those solvable by MWRP-CP3. See mwrp-cp3.github.io for the open source codebase and video demonstrations.

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 gives practical speedups for multiple watchman routes on 2D grids through state pruning and a new optimal planner, plus bounded suboptimal methods that reach larger instances.

read the letter

The main thing to know is that MWRP-CP3 cuts the search space by more than 95 percent and runs over 200 times faster than prior optimal solvers on grid maps, while the suboptimal variants handle maps three times larger with explicit quality bounds. This comes from pruning areas that are guaranteed visible en route under the grid visibility model, then folding those rules into an improved A*-style planner with better heuristics. MxWA* extends weighted A* to makespan objectives with provable bounds, and they add anytime versions plus a decomposition step to polish existing solutions. The open-source code and demos make the results checkable without guesswork. These pieces are new in combination for the watchman literature, and the empirical numbers on standard grids back the speed claims directly. The pruning and bounds are the parts that stand out as useful engineering advances rather than just another heuristic tweak. The soft spot is that the pruning rules are tied to discrete 2D grid visibility, so they may need reworking for continuous spaces or different sensor models. The experiments also stay inside the watchman route citations, leaving open how the approach compares to other recent multi-robot coverage planners. Nothing in the claims looks internally inconsistent or unfalsifiable. This is for people working on multi-agent coverage and surveillance planning who need solvers that scale on grids with some guarantees attached. A reader who builds or benchmarks these kinds of algorithms will get concrete tools and numbers to work with. It has enough technical substance and validation to deserve a serious referee rather than a quick desk reject.

Referee Report

0 major / 2 minor

Summary. The manuscript introduces pruning techniques to reduce the state space for the Multiple Watchman Route Problem (MWRP) by eliminating map areas guaranteed to be visible en route under a grid visibility model. It proposes MWRP-CP3 as an optimal planner integrating these prunings with enhanced heuristics, along with suboptimal algorithms such as MxWA* that provide provable quality bounds, anytime variants, and decomposition-based improvement methods. Empirical evaluations on 2D grid maps demonstrate that MWRP-CP3 achieves over 95% search space reduction and more than 200x speedup compared to prior optimal solvers, while suboptimal methods handle instances three times larger.

Significance. If the pruning rules preserve optimality and the quality bounds are correctly derived, this advances practical multi-agent coverage planning in robotics by enabling larger instances to be solved with performance guarantees. The open-source codebase, video demonstrations, and focus on both optimal and bounded-suboptimal methods with reproducible results are clear strengths that support adoption and extension in heuristic search for coverage problems.

minor comments (2)

[Abstract] Abstract: the statement that suboptimal algorithms have 'bounds on solution quality' would benefit from briefly indicating the form of the bounds (e.g., approximation ratio or additive) to give readers an immediate sense of the guarantees.
[Methods] The pruning methods rely on the specific 2D grid visibility model; a short formal statement of the visibility assumption in the methods section would help readers assess applicability to other environments.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their supportive summary of the manuscript and for recommending minor revision. We are pleased that the significance of the pruning techniques, MWRP-CP3, the provable bounds on suboptimal methods, and the empirical results on search-space reduction and scalability are recognized. Since the report lists no specific major comments, we have no individual points to rebut and will incorporate any minor editorial or presentation improvements in the revised version.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's core contributions consist of pruning rules for visibility in grid maps, an A*-based optimal planner (MWRP-CP3), weighted-A* variants with explicit quality bounds, and anytime/decomposition techniques. These rest on standard heuristic search machinery and provable dominance arguments under the stated visibility model; none of the performance claims or optimality guarantees reduce by construction to fitted parameters, self-definitional loops, or load-bearing self-citations. The derivation chain is self-contained and externally verifiable via the supplied open-source implementation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard graph-search assumptions and a domain-specific visibility model for 2D grids; no free parameters or invented entities are introduced.

axioms (2)

standard math A* search with admissible heuristics yields optimal solutions when used with the described cost function
Invoked for the optimality guarantees of MWRP-CP3 and the bounds of MxWA*.
domain assumption Visibility in 2D grid maps permits safe pruning of areas seen en route to other locations
Central to the state-space reduction technique described in the abstract.

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discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

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