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Many NP-complete problems take integers as part of their input instances.These input integers are generally binarized, that is, provided in the form ofthe "binary" numeral representation, and the lengths of such binary forms areused as a basis unit to measure the computational complexity of the problems.In sharp contrast, the "unarization" (or the "unary" numeral representation) ofnumbers has been known to bring a remarkably different effect onto thecomputational complexity of the problems. When no computational-complexitydifference is observed between binarization and unarization of instances, onthe contrary, the problems are said to be strong NP-complete. This workattempts to spotlight an issue of how the unarization of instances affects thecomputational complexity of various combinatorial problems. We present numerousNP-complete (or even NP-hard) problems, which turn out to be easily solvablewhen input integers are represented in unary. We then discuss the computationalcomplexities of such problems when taking unary-form integer inputs. We hopethat a list of such problems signifies the structural differences betweenstrong NP-completeness and non-strong NP-completeness.

When Input Integers are Given in the Unary Numeral Representation