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The problem of writing high performance parallel applications becomes even more challenging when irregular, sparse or adaptive methods are employed. In this paper we introduce compiler and runtime support for programs with indirect array accesses into Titanium, a high-level language that combines an explicit SPMD parallelism model with implicit communication through a global shared address space. By combining the well-known inspectorexecutor technique with high level multi-dimensional array constructs, compiler analysis and performance modeling, we demonstrate optimizations that are entirely hidden from the programmer. The global address space makes the programs easier to write than in message passing, with remote array accesses used in place of explicit messages with data packing and unpacking. The programs are also faster than message passing programs: Using sparse matrixvector multiplication programs, we show that the Titanium code is an average of 21% faster across several matrices and machines, with the best case speedup more than a factor of 2x. The performance advantages are due to both the lightweight RDMA (Remote Direct Memory Access) communication model that underlies the Titanium implementation and automatic optimization selection that adapts the communication to the machine and workload, in some cases using different communication models for different processors within a single computation.