arXiv subjects

H. Van Dyke Parunak

Publications and source records attributed to H. Van Dyke Parunak.

3 recordsLinked to original sources

arXiv2026

Stigmergic Swarming Agents for Fast Subgraph Isomorphism

Maximum partial subgraph isomorphism compares two graphs (nodes joined by edges) to find a largest common subgraph. A common use case, for graphs with labeled nodes, seeks to find instances of a \textit{query} graph with $q$ nodes in a (typically larger) \textit{data} graph with $d$ nodes. The problem is NP-complete, and naïve solutions are exponential in $q + d$. The fastest current heuristic has complexity $O(d^2)$. This paper outlines ASSIST (Approximate Swarming Subgraph Isomorphism through Stigmergy), inspired by the ant colony optimization approach to the traveling salesperson. After peering (identifying matching individual nodes in query and data) in time $O(q\cdot log(d))$, the time required for ASSIST's iterative subgraph search, the combinatorially complex part of the problem, is linear in query size and constant in data size. ASSIST can be extended to support matching problems (such as temporally ordered edges, inexact matches, and missing nodes or edges in the data graph) that frustrate other heuristics.

cs.MA↗

arXiv2025

$O(p \log d)$ Subgraph Isomorphism using Stigmergic Swarming Agents

Subgraph isomorphism compares two graphs (sets of nodes joined by edges) to determine whether they contain a common subgraph. Many applications require identifying the subgraph, not just deciding its existence. A particularly common use case, using graphs with labeled nodes, seeks to find instances of a smaller pattern graph with $p$ nodes in the larger data graph with $d$ nodes. The problem is NP-complete, so that naïve solutions are exponential in $p + d$. A wide range of heuristics have been proposed, with the best complexity $O(p^2d^2)$. This paper outlines ASSIST (Approximate Swarming Subgraph Isomorphism through Stigmergy), inspired by the ant colony optimization approach to the traveling salesperson problem. ASSIST is linearithmic, $O(p \log d)$, and also supports matching problems (such as temporally ordered edges, inexact matches, and missing nodes or edges in the data graph) that frustrate other heuristics.

cs.MA↗

arXiv2003

Phase Structures of Resource Allocation Games

We consider a class of games that are generalizations of the minority game, in that the demand and supply of the resource are specified independently. This allows us to study systems in which agents compete for a resource under different demand loads. Among other features, we find, using numerical simulations the existence of a robust phase change with a coexistence region as the demand load is varied, separating regions with nearly balanced supply and demand from regions of scarce or abundant resources. The coexistence region exists when the amount of information used by the agents to make their choices is greater than a critical value, which is related to the point at which there is a phase transition in the standard minority game.

nlin.AO↗