# An exact algorithm for the statistical shortest path problem

Liang Deng, Martin D.F. Wong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

## Abstract

Graph algorithms are widely used in VLSI CAD. Traditional graph algorithms can handle graphs with deterministic edge weights. As VLSI technology continues to scale into nanometer designs, we need to use probability distributions for edge weights in order to model uncertainty due to parameter variations. In this paper, we consider the statistical shortest path (SSP) problem. Given a graph G, the edge weights of G are random variables. For each path P in G, let L P be its length, which is the sum of all edge weights on P. Clearly LP is a random variable and we let μP and σP2 be its mean and variance, respectively. In the SSP problem, our goal is to find a path P connecting two given vertices to minimize the cost function μP + Φ(σP 2) where Φ is an arbitrary function. (For example, if Φ (x) = 3√x, the cost function is μP + 3σP.) To minimize uncertainty in the final result, it is meaningful to look for paths with bounded variance, i.e., σP2 ≤ B for a given fixed bound B. In this paper, we present an exact algorithm to solve the SSP problem in O(B(V + E)) time where V and E are the numbers of vertices and edges, respectively, in G. Our algorithm is superior to previous algorithms for SSP problem because we can handle: 1) general graphs (unlike previous works applicable only to directed acyclic graphs), 2) arbitrary edge-weight distributions (unlike previous algorithms designed only for specific distributions such as Gaussian), and 3) general cost function (none of the previous algorithms can even handle the cost function μP + 3σP. Finally, we discuss applications of the SSP problem to maze routing, buffer insertions, and timing analysis under parameter variations.

Original language English (US) Proceedings of the ASP-DAC 2006 Asia and South Pacific Design Automation Conference 2006 Institute of Electrical and Electronics Engineers Inc. 965-970 6 0780394518, 9780780394513 https://doi.org/10.1145/1118299.1118515 Published - 2006 ASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006 - Yokohama, JapanDuration: Jan 24 2006 → Jan 27 2006

### Publication series

Name Proceedings of the Asia and South Pacific Design Automation Conference, ASP-DAC 2006

### Other

Other ASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006 Japan Yokohama 1/24/06 → 1/27/06

## ASJC Scopus subject areas

• Computer Science Applications
• Computer Graphics and Computer-Aided Design
• Electrical and Electronic Engineering

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