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This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems.…
To solve the big topic modeling problem, we need to reduce both time and space complexities of batch latent Dirichlet allocation (LDA) algorithms. Although parallel LDA algorithms on the multi-processor architecture have low time and space…
With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model…
Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a quantum algorithm of Arvind et al.…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
Quantum algorithms for solving noisy linear problems are reexamined, under the same assumptions taken from the existing literature. The findings of this work include on the one hand extended applicability of the quantum Fourier transform to…
We consider the problem of designing and analyzing differentially private algorithms that can be implemented on {\em discrete} models of computation in {\em strict} polynomial time, motivated by known attacks on floating point…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to…
We propose a protocol to solve Leader Election within weak communication models such as the beeping model or the stone-age model. Unlike most previous work, our algorithm operates on only six states, does not require unique identifiers, and…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…
We prove the first, even super-polynomial, lower bounds on the size of tropical (min,+) and (max,+) circuits approximating given optimization problems. Many classical dynamic programming (DP) algorithms for optimization problems are pure in…
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…
This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in networks. Our main result is a randomized…
Many tasks executed in dynamic distributed systems, such as sensor networks or enterprise environments with bring-your-own-device policy, require central coordination by a leader node. In the past it has been proven that distributed leader…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…