Compilers use software-controlled local memories to provide fast, predictable, and power efficient access to critical data. We show that the local-memory allocation for straight-line, or linearized programs is equivalent to a weighted interval-graph coloring problem. This problem is new when allowing a color interval to ''wrap around,'' and we call it the \submarine{} problem. This graph-theoretical decision problem differs slightly from the classical \ship{} problem, and exhibits very interesting and unusual complexity properties. We demonstrate that the \submarine{} problem is NP-complete, while it is solvable in linear time for not-so-proper interval graphs, an extension of the the class of proper interval graphs. We propose a clustering heuristic to approximate any interval graph into a not-so-proper interval graph, decoupling spill code generation from \spm{} assignment. We apply this heuristic to a large number of randomly generated interval graphs reproducing the statistical features of standard \spm{} allocation benchmarks, comparing with state-of-the-art heuristics.