A data-graph computation -popularized by such programming systems as Galois, Pregel, GraphLab, PowerGraph, and GraphChi -is an algorithm that performs local updates on the vertices of a graph. During each round of a data-graph computation, an update function atomically modifies the data associated with a vertex as a function of the vertex's prior data and that of adjacent vertices. A dynamic data-graph computation updates only an active subset of the vertices during a round, and those updates determine the set of active vertices for the next round.This paper introduces PRISM, a chromatic-scheduling algorithm for executing dynamic data-graph computations. PRISM uses a vertex-coloring of the graph to coordinate updates performed in a round, precluding the need for mutual-exclusion locks or other nondeterministic data synchronization. A multibag data structure is used by PRISM to maintain a dynamic set of active vertices as an unordered set partitioned by color. We analyze PRISM using work-span analysis. Let G = (V, E) be a degree-∆ graph colored with χ colors, and suppose that Q ⊆ V is the set of active vertices in a round. Define size(Q) = |Q| + v∈Q deg(v), which is proportional to the space required to store the vertices of Q using a sparsegraph layout. We show that a P-processor execution of PRISM performs updates in Q using O(χ(lg(Q/χ) + lg ∆) + lg P) span and Θ(size(Q) + χ + P) work. These theoretical guarantees are matched by good empirical performance. We modified GraphLab to incorporate PRISM and studied seven application benchmarks on a 12-core multicore machine. PRISM executes the benchmarks 1.2-2.1 times faster than GraphLab's nondeterministic lock-based scheduler while providing deterministic behavior. This paper also presents PRISM-R, a variation of PRISM that executes dynamic data-graph computations deterministically even when updates modify global variables with associative operations. PRISM-R satisfies the same theoretical bounds as PRISM, but its implementation is more involved, incorporating a multivector data structure to maintain an ordered set of vertices partitioned by color.