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• W3201844315 abstract "In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov chain Monte Carlo methods for doing so that are based on sampling and splitting random spanning trees. Empirical evidence suggests that the distributions such algorithms sample from place higher weight on more compact redistricting plans, which is a practically useful and desirable property. In this paper, we confirm these observations analytically, establishing an inverse exponential relationship between the total length of the boundaries separating districts and the probability that such a map will be sampled. This result provides theoretical underpinnings for algorithms that are already making a significant real-world impact." @default.
• W3201844315 created "2021-10-11" @default.
• W3201844315 creator A5035370064 @default.
• W3201844315 creator A5041089506 @default.
• W3201844315 date "2021-09-27" @default.
• W3201844315 modified "2023-09-27" @default.
• W3201844315 title "Compact Redistricting Plans Have Many Spanning Trees." @default.
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