random walk is continued. This showed that SL is contained in RLP, the class of problems solvable in polynomial time and logarithmic space with probabilistic machines that reject incorrectly less than 1/3 of the time. By replacing the random walk by a universal traversal sequence, Aleliunas et al. also showed that SL is contained in L/poly, a non-uniform complexity class of the problems solvable deterministically in logarithmic space with polynomial advice. In 1989, Borodin et al. strengthened this result by showing that the complement of USTCON, determining whether two vertices are in different connected components, is also in RLP. This placed USTCON, and SL, in co-RLP and in the intersection of RLP and co-RLP, which is ZPLP, the class of problems which have log-space, expected polynomial-time, no-error randomized algorithms. In 1992, Nisan, Szemerédi, and Wigderson finally found a new deterministic algorithm to solve USTCON using only log1.5 n space. This was improved slightly, but there would be no more significant gains until Reingold. In 1995, Nisan and Ta-Shma showed the surprising result that SL is closed under complement, which at the time was believed by many to be false; that is, SL = co-SL. Equivalently, if a problem can be solved by reducing it to a graph and asking if two vertices are in the same component, it can also be solved by reducing it to another graph and asking if two vertices are in different components. However, Reingold's paper would later make this result redundant. One of the most important corollaries of SL = co-SL is that LSL = SL; that is, a deterministic, log-space machine with an oracle for SL can solve problems in SL (trivially) but cannot solve any other problems. This means it does not matter whether we use Turing reducibility or many-one reducibility to show a problem is in SL; they are equivalent. A breakthrough October 2004 paper by Omer Reingold showed that USTCON is in fact in L. Since USTCON is SL-complete, this implies that SL = L, essentially eliminating the usefulness of consideration of SL as a separate class. A few weeks later, graduate student Vladimir Trifonov showed that USTCON could be solved deterministically using space—a weaker result—using different techniques. There has not been substantial effort into turning Reingold's algorithm for USTCON into a practical formulation. It is explicit in his paper (and those leading up to it) that they are primarily concerned