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A "patch-and-stitchrdquo localization algorithm divides the network into small overlapping subregions. Typically, each subregion consists of a node and all or some of its neighbors. For each subregion, the algorithm builds a local map, called a patch, which is actually an embedding of the nodes it spans in a relative coordinate system. Finally, the algorithm stitches those patches to form a single global map. In a patch-and-stitch algorithm, the stitching order makes an influence on both the performance and the complexity of the algorithm. In this paper, we present a formal framework to deal with stitching orders in patch-and-stitch localization algorithms. In our framework, the stitching order is determined by a stitching scheme and the stitching scheme consists of a stitching policy and a potential function. The potential function is to predict how well a patch will be stitched if patches are stitched according to a given partial order. The stitching policy is a mechanism that determines the stitching order based on the predictions by the potential function. We present various stitching schemes and evaluate them through simulations. In addition, we apply the patch-and-stitch strategy into the anchor-based localization and propose a clustering-based localization algorithm. A potential function is used to partition the network into clusters each of which is centered at an anchor node. For each cluster, a cluster map is constructed via the anchor-free localization algorithm. Then, those cluster maps are combined to form a single global map. We propose a stitching technique for combining those cluster maps and analyze the performance of the algorithm by simulations.