714 research outputs found
Dynamic Graph Queries
Graph databases in many applications - semantic web, transport or biological networks among others - are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries often combine first-order and navigational features.
Motivated by recent results on maintaining dynamic reachability, we study the dynamic evaluation of traditional query languages for graphs in the descriptive complexity framework. Our focus is on maintaining regular path queries, and extensions thereof, by first-order formulas. In particular we are interested in path queries defined by non-regular languages and in extended conjunctive regular path queries (which allow to compare labels of paths based on word relations). Further we study the closely related problems of maintaining distances in graphs and reachability in product graphs.
In this preliminary study we obtain upper bounds for those problems in restricted settings, such as undirected and acyclic graphs, or under insertions only, and negative results regarding quantifier-free update formulas. In addition we point out interesting directions for further research
Dynamic Complexity under Definable Changes
This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. (2) Context-free languages are first-order maintainable under EFO-defined changes. These results are complemented by several inexpressibility results, for example, that the reachability query cannot be maintained by quantifier-free programs under definable, quantifier-free deletions
The Complexity of Kings
A king in a directed graph is a node from which each node in the graph can be
reached via paths of length at most two. There is a broad literature on
tournaments (completely oriented digraphs), and it has been known for more than
half a century that all tournaments have at least one king [Lan53]. Recently,
kings have proven useful in theoretical computer science, in particular in the
study of the complexity of the semifeasible sets [HNP98,HT05] and in the study
of the complexity of reachability problems [Tan01,NT02].
In this paper, we study the complexity of recognizing kings. For each
succinctly specified family of tournaments, the king problem is known to belong
to [HOZZ]. We prove that this bound is optimal: We construct a
succinctly specified tournament family whose king problem is
-complete. It follows easily from our proof approach that the problem
of testing kingship in succinctly specified graphs (which need not be
tournaments) is -complete. We also obtain -completeness
results for k-kings in succinctly specified j-partite tournaments, , and we generalize our main construction to show that -completeness
holds for testing k-kingship in succinctly specified families of tournaments
for all
Traversability, Reconfiguration, and Reachability in the Gadget Framework
Consider an agent traversing a graph of "gadgets", each with local state that
changes with each traversal by the agent. We characterize the complexity of
universal traversal, where the goal is to traverse every gadget at least once,
for DAG gadgets, one-state gadgets, and reversible deterministic gadgets. We
also study the complexity of reconfiguration, where the goal is to bring the
system of gadgets to a specified state, proving many cases PSPACE-complete, and
showing in some cases that reconfiguration can be strictly harder than
reachability (where the goal is for the agent to reach a specified location),
while in other cases, reachability is strictly harder than reconfiguration.Comment: Full version of article appearing in WALCOM 2022. 23 pages, 14
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