Related papers: Average sensitivity of the Knapsack Problem
We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
We study a wholesale supply chain ordering problem. In this problem, the supplier has an initial stock, and faces an unpredictable stream of incoming orders, making real-time decisions on whether to accept or reject each order. What makes…
We revisit the classic #Knapsack problem, which asks to count the Boolean points $(x_1,\dots,x_n)\in\{0,1\}^n$ in a given half-space $\sum_{i=1}^nW_ix_i\le T$. This #P-complete problem admits $(1\pm\epsilon)$-approximation. Before this…
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict…
This paper concerns a high-dimensional stochastic programming problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation…
The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism…
In the online simple knapsack problem items are presented in an iterative fashion and an algorithm has to decide for each item whether to reject or permanently include it into the knapsack without any knowledge about the rest of the…
Hierarchical clustering is a widely used method for unsupervised learning with numerous applications. However, in the application of modern algorithms, the datasets studied are usually large and dynamic. If the hierarchical clustering is…
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…
We consider an issue of much current concern: could fairness, an issue that is already difficult to guarantee, worsen when algorithms run much of our lives? We consider this in the context of resource-allocation problems, we show that…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
In this paper, we investigate the parametric knapsack problem, in which the item profits are affine functions depending on a real-valued parameter. The aim is to provide a solution for all values of the parameter. It is well-known that any…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…