# A sublinear space, polynomial time algorithm for directed s-t connectivity

@article{Barnes1992ASS, title={A sublinear space, polynomial time algorithm for directed s-t connectivity}, author={Greg Barnes and Jonathan F. Buss and Walter L. Ruzzo and Baruch Schieber}, journal={[1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference}, year={1992}, pages={27-33} }

A deterministic sublinear space, polynomial-time algorithm for directed s-t connectivity, which is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph, is presented. For n-vertex graphs, the algorithm can use as little as n/2/sup Theta /( square root log n) space while still running in polynomial time.<<ETX>>

## 77 Citations

### Undirecteds-t connectivity in polynomial time and sublinear space

- Computer Sciencecomputational complexity
- 2005

This paper presents the first known deterministic algorithms solving undirecteds-t connectivity using sublinear space and polynomial time, and provides a nearly smooth time-space tradeoff between depth-first search and Savitch's algorithm.

### Relating Sublinear Space Computability Among Graph Connectivity and Related Problems

- Computer Science, MathematicsSOFSEM
- 2016

Algorithmic techniques are demonstrated to relate the sublinear-space computability of directed graph connectivity and undirected graph length bounded connectivity and the number n of vertices w.r.t. the number of vertice.

### Õ(√n)-Space and Polynomial-Time Algorithm for Planar Directed Graph Reachability

- MathematicsMFCS
- 2014

The main result of this paper is to show that the directed graph reachability problem restricted to planar graphs can be solved in polynomial time using only \(\widetilde{O}(\sqrt{n})\) space.

### Time-Space Tradeoffs For Undirected st-Connectivity on a Graph Automata

- Computer ScienceSIAM J. Comput.
- 1998

Any probabilistic jumping automaton for graphs (JAG) requires either space $\Omega( \log^2 n /\log log n )$ or time $n^{(1 + \Omega ( 1 / \log \log n )) }$ to solve undirected st-connectivity.

### An O(nε) Space and Polynomial Time Algorithm for Reachability in Directed Layered Planar Graphs

- MathematicsISAAC
- 2015

It is shown that reachability in directed layered planar graphs can be decided in polynomial time and O(nε) space, for any ε > 0.

### Space-efficient Basic Graph Algorithms

- Computer ScienceSTACS
- 2015

We reconsider basic algorithmic graph problems in a setting where an n-vertex input graph is read-only and the computation must take place in a working memory of O(n) bits or little more than that.…

### STCON in Directed Unique-Path Graphs

- Mathematics, Computer ScienceFSTTCS
- 2008

The results may be viewed along the continuum of sublinear-space polynomial-time algorithms for STCON in different classes of directed graphs - from slightly sub linear-space algorithms for general graphs to O(\log n) space algorithms for trees.

### Algorithms and Lower Bounds for Cycles and Walks: Small Space and Sparse Graphs

- Mathematics, Computer ScienceITCS
- 2020

A reduction is given that connects the running time of undirected 2k-cycle to finding directed odd cycles, s-t connectivity in directed graphs, and Max-3-SAT, and a space-efficient algorithms and conditional time lower bounds for finding cycles and walks in graphs are considered.

### Time-space trade-offs for undirected st-connectivity on a JAG

- Computer ScienceSTOC
- 1993

For every constant z z O, the expected time to solve undirected sr-connectivity on a probabilistic JAG with p ~ & & pebbles and q < n’”< n states isn x ZQ(*J when theinputgraph is chosen unifortnly from a family of 3-regular graphs.

### Randomized Time-Space Tradeoffs for Directed Graph Connectivity

- Computer ScienceFSTTCS
- 2003

This work uses a strategy parameterized by a parameter k that uses k pebbles and performs short random walks of length 1 using a probabilistic counter to get a family of algorithms that ranges between log2 n and log n in space and 2\(^{{\rm log^2}n}\) and n n in running time.

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The authors present a deterministic algorithm for the connectivity problem on undirected graphs that runs in O(log/sup 1.5/n) space. Thus, the recursive doubling technique of Savich (1970) which…

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A process for preparing a B30-threonine-insulin which comprising reacting a des-B30-insulin with an excess amount of threonine derivative in the presence of an enzyme specifically acting on the…

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