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I have a set of polygons and I want to find minimal distances between the edge of each pair of them. It's similar task as in this question:

How to find the minimum edge to edge distance of polygons?

But I'd prefer to make it in QGIS or other free available program. Also I'm very beginner in using geographic information systems software so I'd be really grateful if you make your answer as simple as possible.

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The ST_Distance function in the link you referenced works the same in spatialite. YOu can import your polygons into spatialite and calculate min distances there.

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