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تسجيل مستخدم جديدGraph search via star sampling with and without replacement
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Star sampling (SS) is a random sampling procedure on a graph wherein each sample consists of a randomly selected vertex (the star center) and its (one-hop) neighbors (the star points). We consider the use of SS to find any member of a target set of vertices in a graph, where the figure of merit (cost) is either the expected number of samples (unit cost) or the expected number of star centers plus star points (linear cost) until a vertex in the target set is encountered, either as a star center or as a star point. We analyze these two performance measures on three related star sampling paradigms: SS with replacement (SSR), SS without center replacement (SSC), and SS without star replacement (SSS). Exact and approximate expressions are derived for the expected unit and linear costs of SSR, SSC, and SSS on ErdH{o}s-R{e}nyi (ER) random graphs. The approximations are seen to be accurate. SSC/SSS are notably better than SSR under unit cost for low-density ER graphs, while SSS is notably better than SSR/SSC under linear cost for low- to moderate-density ER graphs. Simulations on twelve real-world graphs shows the cost approximations to be of variable quality: the SSR and SSC approximations are uniformly accurate, while the SSS approximation, derived for an ER graph, is of variable accuracy.
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Star sampling (SS) is a random sampling procedure on a graph wherein each sample consists of a randomly selected vertex (the star center) and its one-hop neighbors (the star endpoints). We consider the use of star sampling to find any member of an ar
bitrary target set of vertices in a graph, where the figure of merit (cost) is either the expected number of samples (unit cost) or the expected number of star centers plus star endpoints (linear cost) until a vertex in the target set is encountered, either as a star center or as a star point. We analyze this performance measure on three related star sampling paradigms: SS with replacement (SSR), SS without center replacement (SSC), and SS without star replacement (SSS). We derive exact and approximate expressions for the expected unit and linear costs of SSR, SSC, and SSS on Erdos-Renyi (ER) graphs. Our results show there is i) little difference in unit cost, but ii) significant difference in linear cost, across the three paradigms. Although our results are derived for ER graphs, experiments on real-world graphs suggest our performance expressions are reasonably accurate for non-ER graphs.
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