When Hashing Met Matching: Efficient Spatio-Temporal Search for Ridesharing

Carpooling, or sharing a ride with other passengers, holds immense potential for urban transportation. Ridesharing platforms enable such sharing of rides using real-time data. Finding ride matches in real-time at urban scale is a difficult combinatorial optimization task and mostly heuristic approaches are applied. In this work, we mathematically model the problem as that of finding near-neighbors and devise a novel efficient spatio-temporal search algorithm based on the theory of locality sensitive hashing for Maximum Inner Product Search (MIPS). The proposed algorithm can find $k$ near-optimal potential matches for every ride from a pool of $n$ rides in time $O(n^{1 + \rho} (k + \log n) \log k)$ and space $O(n^{1 + \rho} \log k)$ for a small $\rho < 1$. Our algorithm can be extended in several useful and interesting ways increasing its practical appeal. Experiments with large NY yellow taxi trip datasets show that our algorithm consistently outperforms state-of-the-art heuristic methods thereby proving its practical applicability

More on a problem of Zarankiewicz

We show tight necessary and sufficient conditions on the sizes of small bipartite graphs whose union is a larger bipartite graph that has no large bipartite independent set. Our main result is a common generalization of two classical results in graph theory: the theorem of Kovari, Sos and Turan on the minimum number of edges in a bipartite graph that has no large independent set, and the theorem of Hansel (also Katona and Szemeredi and Krichevskii) on the sum of the sizes of bipartite graphs that can be used to construct a graph (non-necessarily bipartite) that has no large independent set. Our results unify the underlying combinatorial principles developed in the proof of tight lower bounds for depth-two superconcentrators

Secure and Efficient Multi-Key FHE Scheme Supporting Multi-bit Messages from LWE Preserving Non-Interactive Decryption

We consider multi-key fully homomorphic encryption (multi-key FHE) which is the richest variant of fully homomorphic encryption (FHE) that allows complex computation on encrypted data under different keys. Since its introduction by Lopez-Alt, Tromer and Vaikuntanathan in 2012, numerous proposals have been presented yielding various improvements in security and efficiency. However, most of these multi-key FHE schemes encrypt a single-bit message. Constructing a multi-key FHE scheme encrypting multi-bit messages have been notoriously difficult without loosing efficiency for homomorphic evaluation and ciphertext extension under additional keys. In this work, we study multi-key FHE that can encrypt multi-bit messages. Motivated by the goals of improving the efficiency, we propose a new construction with non-interactive decryption and security against chosen-plaintext attack (IND-CPA) from the standard learning with errors (LWE) assumption. We consider a binary matrix as plaintext instead of a single-bit. Our approach supports efficient homomorphic matrix addition and multiplication. Another interesting feature is that our technique of extending a ciphertext under additional keys yields significant reduction in the computational overhead. More interestingly, when contrasted with the previous multi-key FHE schemes for multi-bit messages, our candidates exhibits favorable results in the length of the secret key, public key and ciphertext preserving non-interactive decryption. Keywords: lattice based cryptosystem, multi-key fully homomorphic encryption, learning with errors, multi-bit message