The total biharmonic distance, which is the sum of the biharmonic distance between every pair of nodes in a network, is a key metric for evaluating network connectivity and robustness. In this paper, we study the problem of minimizing the total biharmonic distance by adding k nonexistent edges for a given graph G and budget k. The problem is computationally challenging. We show that the objective function of the problem is monotone but not supermodular. To solve this problem, we propose simple greedy algorithms with cubic time complexity. To mitigate the high time complexity of these greedy algorithms, we apply several techniques, including the projection method, the Laplacian solver, and convex hull approximation. These techniques reduce the time complexity of our proposed algorithms from cubic to nearly linear while providing error guarantees. Finally, extensive experiments on real datasets demonstrate both the efficiency and effectiveness of our proposed algorithms.

The current blockchain system suffers from serious scalability bottleneck, which greatly limits the application in large-scale. Furthermore, with the emergence of high-throughput consensus algorithms in permissioned blockchain, how to efficiently execute smart contracts becomes a critical challenge. To solve this issue, a two-phase concurrent execution mechanism has been adopted recently, where the primary executes a batch of transactions concurrently in the first phase, then the rest replays them in the second phase to achieve consistency. However, these works only enable intra-node concurrency, not inter-node concurrency. This demonstration showcases SEFrame, a novel execution framework for smart contracts of permissioned blockchain to achieve intra- and inter-node concurrency with the confidentiality guarantee of Intel Software Guard Extensions (SGX). We use real-time dashboards containing the output of SEFrame, which allows attendees to interactively explore how SEFrame achieves efficient inter- and intra-node concurrency.