---
_id: '5441'
abstract:
- lang: eng
text: We study algorithmic questions for concurrent systems where the transitions
are labeled from a complete, closed semiring, and path properties are algebraic
with semiring operations. The algebraic path properties can model dataflow analysis
problems, the shortest path problem, and many other natural problems that arise
in program analysis. We consider that each component of the concurrent system
is a graph with constant treewidth, a property satisfied by the controlflow graphs
of most programs. We allow for multiple possible queries, which arise naturally
in demand driven dataflow analysis. The study of multiple queries allows us to
consider the tradeoff between the resource usage of the one-time preprocessing
and for each individual query. The traditional approach constructs the product
graph of all components and applies the best-known graph algorithm on the product.
In this approach, even the answer to a single query requires the transitive closure
(i.e., the results of all possible queries), which provides no room for tradeoff
between preprocessing and query time. Our main contributions are algorithms that
significantly improve the worst-case running time of the traditional approach,
and provide various tradeoffs depending on the number of queries. For example,
in a concurrent system of two components, the traditional approach requires hexic
time in the worst case for answering one query as well as computing the transitive
closure, whereas we show that with one-time preprocessing in almost cubic time,
each subsequent query can be answered in at most linear time, and even the transitive
closure can be computed in almost quartic time. Furthermore, we establish conditional
optimality results showing that the worst-case running time of our algorithms
cannot be improved without achieving major breakthroughs in graph algorithms (i.e.,
improving the worst-case bound for the shortest path problem in general graphs).
Preliminary experimental results show that our algorithms perform favorably on
several benchmarks.
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Amir
full_name: Goharshady, Amir
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Andreas
full_name: Pavlogiannis, Andreas
id: 49704004-F248-11E8-B48F-1D18A9856A87
last_name: Pavlogiannis
orcid: 0000-0002-8943-0722
citation:
ama: Chatterjee K, Ibsen-Jensen R, Goharshady AK, Pavlogiannis A. Algorithms
for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components.
IST Austria; 2015. doi:10.15479/AT:IST-2015-340-v1-1
apa: Chatterjee, K., Ibsen-Jensen, R., Goharshady, A. K., & Pavlogiannis, A.
(2015). Algorithms for algebraic path properties in concurrent systems of constant
treewidth components. IST Austria. https://doi.org/10.15479/AT:IST-2015-340-v1-1
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Amir Kafshdar Goharshady,
and Andreas Pavlogiannis. Algorithms for Algebraic Path Properties in Concurrent
Systems of Constant Treewidth Components. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-340-v1-1.
ieee: K. Chatterjee, R. Ibsen-Jensen, A. K. Goharshady, and A. Pavlogiannis, Algorithms
for algebraic path properties in concurrent systems of constant treewidth components.
IST Austria, 2015.
ista: Chatterjee K, Ibsen-Jensen R, Goharshady AK, Pavlogiannis A. 2015. Algorithms
for algebraic path properties in concurrent systems of constant treewidth components,
IST Austria, 24p.
mla: Chatterjee, Krishnendu, et al. Algorithms for Algebraic Path Properties
in Concurrent Systems of Constant Treewidth Components. IST Austria, 2015,
doi:10.15479/AT:IST-2015-340-v1-1.
short: K. Chatterjee, R. Ibsen-Jensen, A.K. Goharshady, A. Pavlogiannis, Algorithms
for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components,
IST Austria, 2015.
date_created: 2018-12-12T11:39:21Z
date_published: 2015-07-11T00:00:00Z
date_updated: 2023-09-19T14:36:19Z
day: '11'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2015-340-v1-1
file:
- access_level: open_access
checksum: df383dc62c94d7b2ea639aba088a76c6
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:54:09Z
date_updated: 2020-07-14T12:46:56Z
file_id: '5531'
file_name: IST-2015-340-v1+1_main.pdf
file_size: 861396
relation: main_file
file_date_updated: 2020-07-14T12:46:56Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '24'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '340'
related_material:
record:
- id: '1437'
relation: later_version
status: public
- id: '5442'
relation: earlier_version
status: public
- id: '6009'
relation: later_version
status: public
status: public
title: Algorithms for algebraic path properties in concurrent systems of constant
treewidth components
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...