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A reduction of the logspace shortest path problem to biconnected graphs

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Boris Brimkov

Computational Complexity · Submitted 23 Nov 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs.

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arXiv ID1511.07100 (version 1)
Pith IDG6BUQWDW, Pith's permanent record of this paper and its review
CitationBoris Brimkov. "A reduction of the logspace shortest path problem to biconnected graphs." arXiv:1511.07100 (2015). https://pith.science/paper/G6BUQWDW
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,977 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.71 · compares with prior results 0.42 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. The asymptotic time-space product of this algorithm is the best possible among all shortest path algorithms.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. contribution 1.00 0.95 0.85 asserted 1.00
s1 We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. contribution 0.98 0.95 0.11 asserted 1.00
s2 The asymptotic time-space product of this algorithm is the best possible among all shortest path algorithms. result 0.82 0.80 0.21 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.68 · evidence from proof or derivation 1.00.

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. The asymptotic time-space product of this algorithm is the best possible among all shortest path algorithms.

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