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We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of m linear inequalities on n real variables with at most two variables per inequality (2VPI). We give a randomized trade-off algorithm solving both problems and running in Õ(nmh+(n/h)^3) time using Õ(n^2/h+m) space for any parameter h∈ [1,n]. In particular, using subquadratic space we get Õ(nm+n^3/2m^3/4) running time, whicharXiv:2110.15070v1 fatcat:ysvlyez4cnegzfqlodl7675wom