Related papers: Space--Time Tradeoffs for Subset Sum: An Improved …
We provide improved space-time tradeoffs for permutation problems over additively idempotent semi-rings. In particular, there is an algorithm for the Traveling Salesperson Problem that solves $N$-vertex instances using space $S$ and time…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning…
We present an $\mathcal{O}^\star(2^{0.5n})$ time and $\mathcal{O}^\star(2^{0.249999n})$ space randomized algorithm for solving worst-case Subset Sum instances with $n$ integers. This is the first improvement over the long-standing…
In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied…
More than 40 years ago, Schroeppel and Shamir presented an algorithm that solves the Subset Sum problem for $n$ integers in time $O^*(2^{0.5n})$ and space $O^*(2^{0.25n})$. The time upper bound remains unbeaten, but the space upper bound…
We study the problem of finding $K$ collision pairs in a random function $f : [N] \rightarrow [N]$ by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase…
In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing…
This article deals with the spatio-temporal sensors deployment in order to maximize detection probability of an intelligent and randomly moving target in an area under surveillance. Our work is based on the rare events simulation framework.…
In this work, we systematically examine the application of spatio-temporal splitting heuristics to the Multi-Robot Motion Planning (MRMP) problem in a graph-theoretic setting: a problem known to be NP-hard to optimally solve. Following the…
In the Element Distinctness problem, one is given an array $a_1,\dots, a_n$ of integers from $[poly(n)]$ and is tasked to decide if $\{a_i\}$ are mutually distinct. Beame, Clifford and Machmouchi (FOCS 2013) gave a low-space algorithm for…
The traveling salesman problem (TSP) is a cornerstone of combinatorial optimization and has deeply influenced the development of algorithmic techniques in both exact and approximate settings. Yet, improving on the decades-old bounds for…
A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) $n$-input Subset Sum problem that runs in time $2^{(1/2 - c)n}$ for some constant $c>0$. In this paper we give a Subset Sum algorithm with…
In this paper, we investigate space-time tradeoffs for answering Boolean conjunctive queries. The goal is to create a data structure in an initial preprocessing phase and use it for answering (multiple) queries. Previous work has developed…
Given a set of numbers, the $k$-SUM problem asks for a subset of $k$ numbers that sums to zero. When the numbers are integers, the time and space complexity of $k$-SUM is generally studied in the word-RAM model; when the numbers are reals,…
We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works…
We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…
We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…
Many search-based quantum algorithms that achieve a theoretical speedup are not practically relevant since they require extraordinarily long coherence times, or lack the parallelizability of their classical counterparts.This raises the…
3SUM-Indexing is a preprocessing variant of the 3SUM problem that has recently received a lot of attention. The best known time-space tradeoff for the problem is $T S^3 = n^{6}$ (up to logarithmic factors), where $n$ is the number of input…