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Traveling Salesman Problem (TSP) is a classical NP-complete problem in graph theory. It aims at finding a least-cost Hamiltonian cycle that traverses all vertices of an input edge-weighted graph. One application of TSP is in breakpoint median-based Maximum Parsimony phylogenetic tree reconstruction, wherein a bounded edge-weight model is used. Exponential algorithms that apply efficient heuristics, such as branch-and-bound, to dynamically prune the search space are used. We adopted this approach in an NoC-based implementation for solving TSP targeted towards phylogenetics taking advantage of the fine-grained parallelism and efficient communication network. The largest fraction of the solution time for TSP is accounted for by a particular lower bound calculation operation that uses the graph's adjacency matrix. In this paper, we present the design and implementation of the processing elements with a highly optimized lower bound computation kernel and evaluate its performance. Additionally, we explore two major NoC architectures -mesh and quad-tree - and show that the latter is more suitable for this application domain.