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Numerically efficient and stable algorithms are essential for kernel-based regularized system identification. The state of art algorithms exploit the semiseparable structure of the kernel and are based on the generator representation of the…
Recently cloud-based graph convolutional network (GCN) has demonstrated great success and potential in many privacy-sensitive applications such as personal healthcare and financial systems. Despite its high inference accuracy and…
We survey the field of algorithms and complexity for graph problems parameterized above or below guaranteed values, a research area which was pioneered by Venkatesh Raman. Those problems seek, for a given graph $G$, a solution whose value…
Integer coefficient selection is an important decoding step in the implementation of compute-and-forward (C-F) relaying scheme. Choosing the optimal integer coefficients in C-F has been shown to be a shortest vector problem (SVP) which is…
The nearest neighbor (NN) technique is very simple, highly efficient and effective in the field of pattern recognition, text categorization, object recognition etc. Its simplicity is its main advantage, but the disadvantages can't be…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
Approximate Nearest Neighbor Search (ANNS) is a cornerstone algorithm for information retrieval, recommendation systems, and machine learning applications. While x86-based architectures have historically dominated this domain, the…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
A long-standing open question in the algorithms and complexity literature is whether there exist sorting circuits of size $o(n \log n)$. A recent work by Asharov, Lin, and Shi (SODA'21) showed that if the elements to be sorted have short…
Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the best algorithm in the literature for solving this problem. In light…
In this paper, first, we utilize the Lowner-John ellipsoid of a convex set to hide the lattice data information. We also describe the algorithm of information recovery in polynomial time by employing the Todd-Khachyian algorithm. The…
The so-called min-sum algorithm has been applied for decoding lattices constructed by Construction D'. We generalize this iterative decoding algorithm to decode lattices constructed by Construction D. An upper bound on the decoding…
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The…
We give a quantum reduction from finding short codewords in a random linear code to decoding for the Hamming metric. This is the first time such a reduction (classical or quantum) has been obtained. Our reduction adapts to linear codes…
Coded blockchains have acquired prominence as a promising solution to reduce storage costs and facilitate scalability. Within this class, Luby Transform (LT) coded blockchains are an appealing choice for scalability owing to the…