Related papers: Quantum and approximation algorithms for maximum w…
The Multiplicative Weights Exponential Mechanism (MWEM) is a fundamental iterative framework for private data analysis, with broad applications such as answering $m$ linear queries, or privately solving systems of $m$ linear constraints.…
Given two sequences $A[1..n]$ and $B[1..m]$ over a totally ordered alphabet, the \emph{Longest Common Bitonic Subsequence} (LCBS) problem asks for a longest common subsequence that is strictly increasing up to a single peak element and…
Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…
A general representation of the quaternion gradients presented in the literature is proposed, and an universal update equation for QLMS-like algorithms is obtained. The general update law is used to study the convergence of widely linear…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
The minimum weight matching (MWM) and maximum likelihood decoding (MLD) are two widely used and distinct decoding strategies for quantum error correction. For a given syndrome, the MWM decoder finds the most probable physical error…
We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…
The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…
This paper proposes a quantum approximate optimization algorithm (QAOA) method for wireless scheduling problems. The QAOA is one of the promising hybrid quantum-classical algorithms for many applications and it provides highly accurate…
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
The $ k $-plex model, which allows each vertex to miss connections with up to $ k $ neighbors, serves as a relaxation of the clique. Its adaptability makes it more suitable for analyzing real-world graphs where noise and imperfect data are…
A witness is a sub-database that preserves the query results of the original database but of much smaller size. It has wide applications in query rewriting and debugging, query explanation, IoT analytics, multi-layer network routing, etc.…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an…