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  • Jinyun Xue
  • 1998
In this paper, we derive, by presenting some suitable notations, three typical graph algorithms and corresponding programs using a unified approach, partition-and-recur. We put emphasis on the derivation rather than the algorithms themselves. The main ideas and ingenuity of these algorithms are revealed by formula deduction. Success in these examples gives(More)
  • Jinyun Xue
  • 1993
The loop invariants take a very important role in the design, proof and derivation of the algorithmic program. We point out the limitations of the traditional standard strategy for developing loop invariants, and propose two new strategies for proving the existing algorithmic program and developing new ones. The strategies use recurrence as vehicle and(More)
  • Jinyun Xue
  • 1997
A unified approach called partition-and-recur for developing efficient and correct algorithmic programs is presented. An algorithm (represented by recurrence and initiation) is separated from program, and special attention is paid to algorithm manipulation rather than program calculus. An algorithm is exactly a set of mathematical formulae. It is easier for(More)
The paper presents a novel approach to formal algorithm design for a typical class of discrete optimization problems. Using a concise set of program calculation rules, our approach reduces a problem into subproblems with less complexity based on function decompositions, constructs the problem reduction graph that describes the recurrence relations between(More)