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In high-speed digital VLSI design, bounding the load capacitance at gate outputs is a well-known methodology to improve coupling noise immunity, reduce degradation of signal transition edges, and reduce delay uncertainty due to coupling noise. Bounding load capacitance also improves reliability with respect to hot-carrier oxide breakdown and AC self-heating in interconnects, and guarantees bounded input rise/fall times at buffers and sinks. This paper introduces a new minimum-buffer routing problem (MBRP) formulation which requires that the capacitive load of each buffer, and of the source driver, be upper-bounded by a given constant. Our contributions are as follows: We give linear-time algorithms for optimal buffering of a given routing tree with a single (inverting or noninverting) buffer type. For simultaneous routing and buffering with a single noninverting buffer type, we prove that no algorithm can guarantee a factor smaller than 2 unless P=NP and give an algorithm with approximation factor slightly larger than 2 for typical buffers. For the case of a single inverting buffer type, we give an algorithm with approximation factor slightly larger than 4. We give local-improvement and clustering based MBRP heuristics with improved practical performance, and present a comprehensive experimental study comparing the runtime/quality tradeoffs of the proposed MBRP heuristics on test cases extracted from recent industrial designs.