Peter J. Downey

Variations on the Common Subexpression Problem

Let G be a directed graph such that for each vertex v in G, the successors of v are ordered Let C be any equivalence relation on the vertices of G. The congruence closure C* of C is the finest equivalence relation containing C and such that any two vertices having corresponding successors equivalent under C* are themselves equivalent under C* Efficient algorithms are described for computing congruence closures in the general case and in the following two special cases. 0) G under C* is acyclic, and (it) G is acychc and C identifies a single pair of vertices. The use of these algorithms to test expression eqmvalence (a problem central to program verification) and to test losslessness of joins in relational databases is described

Computing Sequences with Addition Chains

Given a sequence

Complexity of Task Sequencing with Deadlines, Set-Up Times and Changeover Costs

n_1 , cdots ,n_m

Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

of positive integers, what is the smallest number of additions needed to compute all m integers starting with 1? This generalization of the addition chain (

Probabilistic bounds for dual bin-packing

m = 1

Assignment Commands with Array References

) problem will be called the addition-sequence problem. We show that the sequence

Probabilistic bounds on the performance of list scheduling

{ 2^0 ,2^1 , cdots ,2^{n - 1} ,2^n - 1}

Distribution-free bounds on the expectation of the maximum with scheduling applications

can be computed with

Correct Computation Rules for Recursive Languages

n + 2.13sqrt n + log n

Off-line and on-line algorithms for deducing equalities

additions, and that