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==Properties==
{{See also|Oriented matroid}}
The criss-cross algorithm was published independently by [[Tamás Terlaky]]<ref> {{harvtxt|Terlaky|1985}} and {{harvtxt|Terlaky|1987}} </ref> and by Zhe-Min Wang;<ref name="Wang" >{{harvtxt|Wang|1987}} </ref> related algorithms appeared in unpublished reports by other authors. Their publications considered linear-programming in the abstract setting of [[oriented matroid]]s (OMs).<ref>The theory of oriented matroids was initiated by [[R. Tyrrell Rockafellar]] to describe the sign patterns of the matrices arising through the pivoting operations of Dantzig's simplex algorithm; Rockafellar was inspired by [[Albert W. Tucker]] studies of such sign patterns in "Tucker tableaux". {{harv|Rockafellar|1969}}</ref> Indeed, Bland's pivoting rule was based on his previous papers on oriented matroid theory. Much literature on the criss-cross algorithm concerns oriented matroids. Historically, OM algorithms for [[quadratic programming|quadratic-programming problems]] and [[linear complementarity problem|linear-complementarity problem]]s had been published by [[Michael J. Todd (mathematician)|Michael J. Todd]] before Terlaky and Wang published their criss-cross algorithms.<ref name="Todd" > {{cite
|pages=417–479|doi=10.1017/CBO9780511586507|MR=1744046}}</ref>
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