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The Implicit Factorization Problem was first introduced by May and Ritzenhofen at PKC'09. This problem aims to factorize two RSA moduli $N_1=p_1q_1$ and $N_2=p_2q_2$ when their prime factors share a certain number of least significant bits…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
In many integer factoring algorithms, one produces a sequence of integers (created in a pseudo-random way), and wishes to rapidly determine a subsequence whose product is a square (which we call a square product). In his lecture at the 1994…
We give a polynomial-time approximation algorithm for the (not necessarily metric) $k$-Median problem. The algorithm is an $\alpha$-size-approximation algorithm for $\alpha < 1 + 2 \ln(n/k)$. That is, it guarantees a solution having size at…
Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…
In this paper, we study the single-item economic lot-sizing problem with production cost functions that are piecewise linear. The lot-sizing problem stands as a foundational cornerstone within the domain of lot-sizing problems. It is also…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be…
Let $a,k\in\mathbb{N}$. For the $k-1$-th iterate of the exponential function $x\mapsto a^x$, also known as tetration, we write \[ ^k a:=a^{a^{.^{.^{.^{a}}}}}. \] In this paper, we show how an efficient algorithm for tetration modulo natural…
We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…
In 1937, biologists Sturtevant and Tan posed a computational question: transform a chromosome represented by a permutation of genes, into a second permutation, using a minimum-length sequence of reversals, each inverting the order of a…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
Dang et al. have given an algorithm that can find a Tarski fixed point in a $k$-dimensional lattice of width $n$ using $O(\log^{k} n)$ queries. Multiple authors have conjectured that this algorithm is optimal [Dang et al., Etessami et al.],…
The fermion determinant is a highly non-local object and its logarithm is an extensive quantity. For these reasons it is widely believed that the determinant cannot be treated in acceptance steps of gauge link configurations that differ in…
We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…