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In this paper, we present a reconfigurable architecture for networks-on-chip (NoC) on which arbitrary application-specific topologies can be implemented. When a new application starts, the proposed NoC tailors its topology to the application traffic pattern by changing the inter-router connections to some predefined configuration corresponding to the application. It addresses one of the main drawbacks of the existing application-specific NoC optimization methods, i.e., optimization of NoCs based on the traffic pattern of a single application. Supporting multiple applications is a critical feature of an NoC when several different applications are integrated into a single modern and complex multicore system-on-chip or chip multiprocessor. The proposed reconfigurable NoC architecture supports multiple applications by appropriately configuring itself to a topology that matches the traffic pattern of the currently running application. This paper first introduces the proposed reconfigurable topology and then addresses the problems of core to network mapping and topology exploration. Further on, we evaluate the impact of different architectural attributes on the performance of the proposed NoC. Evaluations consider network latency, power consumption, and area complexity.