  Deutsch-Jozsa (DJ) problem is one of the most important problems
demonstrating the power of quantum algorithm. DJ problem can be described as a
Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is
either constant or balanced, and the purpose is to determine which type it is.
DJ algorithm can solve it exactly with one query. In this paper, we first
discover the inherent structure of DJ problem in distributed scenario by giving
a number of equivalence characterizations between $f$ being constant (balanced)
and some properties of $f$'s subfunctions, and then we propose three
distributed exact quantum algorithms for solving DJ problem. Our algorithms
have essential acceleration over distributed classical deterministic algorithm,
and can be extended to the case of multiple computing nodes. Compared with DJ
algorithm, our algorithms can reduce the number of qubits and the depth of
circuit implementing a single query operator. Therefore, we find that the
structure of problem should be clarified for designing distributed quantum
algorithm to solve it.
