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The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…

Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying…

In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…

We study the problem of computing an approximate maximum cardinality matching in the semi-streaming model when edges arrive in a \emph{random} order. In the semi-streaming model, the edges of the input graph G = (V,E) are given as a stream…

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…

We consider the problem of sketching the $p$-th frequency moment of a vector, $p>2$, with multiplicative error at most $1\pm \epsilon$ and \emph{with high confidence} $1-\delta$. Despite the long sequence of work on this problem, tight…

The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…

Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of…

The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and complexity theory with a wide range of applications. Instead of…

The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…

We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…

Given two polygonal curves $P$ and $Q$ defined by $n$ and $m$ vertices with $m\leq n$, we show that the discrete Fr\'echet distance in 1D cannot be approximated within a factor of $2-\varepsilon$ in $\mathcal{O}((nm)^{1-\delta})$ time for…