Related papers: A Space-space Trade-off for Directed st-Connectivi…
Directed $st$-connectivity (DSTCON) is the problem of deciding if there exists a directed path between a pair of distinguished vertices $s$ and $t$ in an input directed graph. This problem appears in many algorithmic applications, and is…
We develop catalytic algorithms for fundamental problems in algorithm design that run in polynomial time, use only $\mathcal{O}(\log(n))$ workspace, and use sublinear catalytic space matching the best-known space bounds of non-catalytic…
Undirected $st$-connectivity is important both for its applications in network problems, and for its theoretical connections with logspace complexity. Classically, a long line of work led to a time-space tradeoff of $T=\tilde{O}(n^2/S)$ for…
Kallampally and Tewari showed in 2016 that there can be a trade-off between determinism and time in space-bounded computations. This they did by describing an unambiguous non-deterministic algorithm to solve Directed Graph Reachability that…
We present a $\mathsf{BQSPACE}(O(\log n))$-procedure to count $st$-paths on directed graphs for which we are promised that there are at most polynomially many paths starting in $s$ and polynomially many paths ending in $t$. For comparison,…
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…
A celebrated theorem of Savitch states that NSPACE(S) is contained in DSPACE(S^2). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log^2{n}) space, implying NL is in…
We give a deterministic $\tilde{O}(\log n)$-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for…
We give fast, simple, and implementable catalytic logspace algorithms for two fundamental graph problems. First, a randomized catalytic algorithm for $s\to t$ connectivity running in $\widetilde{O}(nm)$ time, and a deterministic catalytic…
We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only $O(s)$ words of workspace in addition to the memory for input. In this…
We revisit a classical graph-theoretic problem, the \textit{single-source shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in $O(n \log^2 n)$ time…
Consider the following "local" cut-detection problem in a directed graph: We are given a seed vertex $x$ and need to remove at most $k$ edges so that at most $\nu$ edges can be reached from $x$ (a "local" cut) or output $\bot$ to indicate…
Let $\mathcal{P}$ be a set of $h$ pairwise-disjoint polygonal obstacles with a total of $n$ vertices in the plane. We consider the problem of building a data structure that can quickly compute an $L_1$ shortest obstacle-avoiding path…
We prove the first polynomial separation between randomized and deterministic time-space tradeoffs of multi-output functions. In particular, we present a total function that on the input of $n$ elements in $[n]$, outputs $O(n)$ elements,…
Due to Savitch's theorem we know $NL\subseteq DSPACE(\log^2(n))$. To show this upper bound, Savitch constructed an algorithm with $O(\log^2(n))$ space on the working tape. We will show that Savitch's algorithm also described a lower bound…
Let $\kappa(s,t)$ denote the maximum number of internally disjoint $st$-paths in an undirected graph $G$. We consider designing a compact data structure that answers $k$-bounded node connectivity queries: given $s,t \in V$ return…
For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are…
We give an $O(n \log \log n)$ time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest $O(n\log^3 n)$ solution. Interestingly, while in…
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set $S$ of $n$ point-sites in the plane. More precisely, we assume that $S$ resides in a random-access memory that can only be read. The edges of the…
In this paper, we discuss an algorithm for the problem of undirected st-connectivity that is deterministic and log-space, namely that of Reingold within his 2008 paper "Undirected Connectivity in Log-Space". We further present a separate…