Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a previous field study, it was observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.
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A Model for Ant Trail Formation and its Convergence Properties
We introduce a model for ant trail formation, building upon previous work on biologically feasible local algorithms that plausibly describe how ants maintain trail networks. The model is a variant of a reinforced random walk on a directed graph, where ants lay pheromone on edges as they traverse them and the next edge to traverse is chosen based on the level of pheromone; this pheromone decays with time. There is a bidirectional flow of ants in the network: the forward flow proceeds along forward edges from source (e.g. the nest) to sink (e.g. a food source), and the backward flow in the opposite direction. Some fraction of ants are lost as they pass through each node (modeling the loss of ants due to exploration observed in the field). We initiate a theoretical study of this model. We note that ant navigation has inspired the field of ant colony optimization, heuristics that have been applied to several combinatorial optimization problems; however the algorithms developed there are considerably more complex and not constrained to being biologically feasible. We first consider the linear decision rule, where the flow divides itself among the next set of edges in proportion to their pheromone level. Here, we show that the process converges to the path with minimum leakage when the forward and backward flows do not change over time. On the other hand, when the forward and backward flows increase over time (caused by positive reinforcement from the discovery of a food source, for example), we show that the process converges to the shortest path. These results are for graphs consisting of two parallel paths (a case that has been investigated before in experiments). Through simulations, we show that these results hold for more general graphs drawn from various random graph models; proving this convergence in the general case is an interesting open problem. Further, to understand the behaviour of other decision rules beyond the linear rule, we consider a general family of decision rules. For this family, we show that there is no advantage of using a non-linear decision rule, if the goal is to find the shortest or the minimum leakage path. We also show that bidirectional flow is necessary for convergence to such paths. Our results provide a plausible explanation for field observations, and open up new avenues for further theoretical and experimental investigation.
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- NSF-PAR ID:
- 10275100
- Date Published:
- Journal Name:
- 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.more » « less
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This data set contains 194778 quasireaction subgraphs extracted from CHO transition networks with 2-6 non-hydrogen atoms (CxHyOz, 2 <= x + z <= 6).
The complete table of subgraphs (including file locations) is in CHO-6-atoms-subgraphs.csv file. The subgraphs are in GraphML format (http://graphml.graphdrawing.org) and are compressed using bzip2. All subgraphs are undirected and unweighted. The reactant and product nodes (initial and final) are labeled in the "type" node attribute. The nodes are represented as multi-molecule SMILES strings. The edges are labeled by the reaction rules in SMARTS representation. The forward and backward reading of the SMARTS string should be considered equivalent.
The generation and analysis of this data set is described in
D. Rappoport, Statistics and Bias-Free Sampling of Reaction Mechanisms from Reaction Network Models, 2023, submitted. Preprint at ChemrXiv, DOI: 10.26434/chemrxiv-2023-wltcrSimulation parameters
- CHO networks constructed using polar bond break/bond formation rule set for CHO.
- High-energy nodes were excluded using the following rules:
(i) more than 3 rings, (ii) triple and allene bonds in rings, (iii) double bonds at
bridge atoms,(iv) double bonds in fused 3-membered rings.
- Neutral nodes were defined as containing only neutral molecules.
- Shortest path lengths were determined for all pairs of neutral nodes.
- Pairs of neutral nodes with shortest-path length > 8 were excluded.
- Additionally, pairs of neutral nodes connected only by shortest paths passing through
additional neutral nodes (reducible paths) were excluded.For background and additional details, see paper above.
This work was supported in part by the National Science Foundation under Grant No. CHE-2227112. -
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Abstract Biological transportation networks must balance competing functional priorities. The self-organizing mechanisms used to generate such networks have inspired scalable algorithms to construct and maintain low-cost and efficient human-designed transport networks. The pheromone-based trail networks of ants have been especially valuable in this regard. Here, we use turtle ants as our focal system: In contrast to the ant species usually used as models for self-organized networks, these ants live in a spatially constrained arboreal environment where both nesting options and connecting pathways are limited. Thus, they must solve a distinct set of challenges which resemble those faced by human transport engineers constrained by existing infrastructure. Here, we ask how a turtle ant colony’s choice of which nests to include in a network may be influenced by their potential to create connections to other nests. In laboratory experiments with
Cephalotes varians andCephalotes texanus , we show that nest choice is influenced by spatial constraints, but in unexpected ways. Under one spatial configuration, colonies preferentially occupied more connected nest sites; however, under another spatial configuration, this preference disappeared. Comparing the results of these experiments to an agent-based model, we demonstrate that this apparently idiosyncratic relationship between nest connectivity and nest choice can emerge without nest preferences via a combination of self-reinforcing random movement along constrained pathways and density-dependent aggregation at nests. While this mechanism does not consistently lead to the de-novo construction of low-cost, efficient transport networks, it may be an effective way to expand a network, when coupled with processes of pruning and restructuring. -
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An interleaved-Dyck (InterDyck) language consists of the interleaving of two or more Dyck languages, where each Dyck language represents a set of strings of balanced parentheses.InterDyck-reachability is a fundamental framework for program analyzers that simultaneously track multiple properly-matched pairs of actions such as call/return, lock/unlock, or write-data/read-data.Existing InterDyck-reachability algorithms are based on the well-known tabulation technique.
This paper presents a new perspective on solving InterDyck-reachability. Our key observation is that for the single-source-single-target InterDyck-reachability variant, it is feasible to summarize all paths from the source node to the target node based on
path expressions . Therefore, InterDyck-reachability becomes an InterDyck-path-recognition problem over path expressions. Instead of computing summary edges as in traditional tabulation algorithms, this new perspective enables us to express InterDyck-reachability as aparenthesis-counting problem, which can be naturally formulated via integer linear programming (ILP).We implemented our ILP-based algorithm and performed extensive evaluations based on two client analyses (a reachability analysis for concurrent programs and a taint analysis). In particular, we evaluated our algorithm against two types of algorithms: (1) the general all-pairs InterDyck-reachability algorithms based on linear conjunctive language (LCL) reachability and synchronized pushdown system (SPDS) reachability, and (2) two domain-specific algorithms for both client analyses. The experimental results are encouraging. Our algorithm achieves 1.42×, 28.24×, and 11.76× speedup for the concurrency-analysis benchmarks compared to all-pair LCL-reachability, SPDS-reachability, and domain-specific tools, respectively; 1.2×, 69.9×, and 0.98× speedup for the taint-analysis benchmarks. Moreover, the algorithm also provides precision improvements, particularly for taint analysis, where it achieves 4.55%, 11.1%, and 6.8% improvement, respectively.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPIcs.ITCS.2021.85
