English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Planting a solution into the random RB model, which is a prototype of randomconstraint satisfaction problem (CSP) with growing domains, can generate veryhard satisfiable CSP benchmarks. We study the solution space structure of theplanted RB model. With constraint density growing, we find that this model goesthrough four phase transitions. In the replica symmetric phase, what we callthe independent phase transition occurs, after which the planted cluster(cluster containing the planted solution) is separated from the giant cluster.Then the solutions except that in the planted cluster go through the sameclustering phase transition and the same satisfiability phase transition as therandom RB model. The planted cluster goes through the isolated phasetransition, after which the planted cluster contains only one solution. Thisphase diagram provides strong evidence that this model can generate very hardsatisfiable CSP benchmarks. For over constraint instances (where the constraintdensity is very large), we find that the configuration space has only a singleenergy valley, which makes the instances tractable. Experiments using BeliefPropagation confirm the locations of the clustering, satisfiability (byconfigurations outside the planted cluster), and isolated phase transitionpoints.

The solution space structure of planted constraint satisfaction problems with growing domains