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Documents authored by Mukherjee, Sayan


Document
Higher Order Bipartiteness vs Bi-Partitioning in Simplicial Complexes

Authors: Marzieh Eidi and Sayan Mukherjee

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)


Abstract
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the construction of complex networks. Another key identifying feature is their Laplacian spectrum as bipartite graphs achieve the maximum possible eigenvalue of graph Laplacian. However, for modeling higher-order connections in complex systems, hypergraphs and simplicial complexes are required due to the limitations of graphs in representing pairwise interactions. In this article, using simple tools from graph theory, we extend the cycle-based characterization from bipartite graphs to those simplicial complexes that achieve the maximum Hodge Laplacian eigenvalue, known as disorientable simplicial complexes. We show that a N-dimensional simplicial complex is disorientable if its down dual graph contains no simple odd cycle of distinct edges and no twisted even cycle of distinct edges. Furthermore, we see that in a N-simplicial complex without twisting cycles, the fewer the number of (non-branching) simple odd cycles in its down dual graph, the closer is its maximum eigenvalue to the possible maximum eigenvalue of Hodge Laplacian. Similar to the graph case, the absence of odd cycles plays a crucial role in solving the bi-partitioning problem of simplexes in higher dimensions.

Cite as

Marzieh Eidi and Sayan Mukherjee. Higher Order Bipartiteness vs Bi-Partitioning in Simplicial Complexes. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 45:1-45:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{eidi_et_al:LIPIcs.SoCG.2025.45,
  author =	{Eidi, Marzieh and Mukherjee, Sayan},
  title =	{{Higher Order Bipartiteness vs Bi-Partitioning in Simplicial Complexes}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{45:1--45:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.45},
  URN =		{urn:nbn:de:0030-drops-231972},
  doi =		{10.4230/LIPIcs.SoCG.2025.45},
  annote =	{Keywords: Bipartite graphs, Simplicial complex, Disorientability, Hodge Laplacian, odd cycles, Twisted cycles, down-dual graph}
}
Document
Reachability for Updatable Timed Automata Made Faster and More Effective

Authors: Paul Gastin, Sayan Mukherjee, and B Srivathsan

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
Updatable timed automata (UTA) are extensions of classical timed automata that allow special updates to clock variables, like x: = x - 1, x : = y + 2, etc., on transitions. Reachability for UTA is undecidable in general. Various subclasses with decidable reachability have been studied. A generic approach to UTA reachability consists of two phases: first, a static analysis of the automaton is performed to compute a set of clock constraints at each state; in the second phase, reachable sets of configurations, called zones, are enumerated. In this work, we improve the algorithm for the static analysis. Compared to the existing algorithm, our method computes smaller sets of constraints and guarantees termination for more UTA, making reachability faster and more effective. As the main application, we get an alternate proof of decidability and a more efficient algorithm for timed automata with bounded subtraction, a class of UTA widely used for modelling scheduling problems. We have implemented our procedure in the tool TChecker and conducted experiments that validate the benefits of our approach.

Cite as

Paul Gastin, Sayan Mukherjee, and B Srivathsan. Reachability for Updatable Timed Automata Made Faster and More Effective. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{gastin_et_al:LIPIcs.FSTTCS.2020.47,
  author =	{Gastin, Paul and Mukherjee, Sayan and Srivathsan, B},
  title =	{{Reachability for Updatable Timed Automata Made Faster and More Effective}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.47},
  URN =		{urn:nbn:de:0030-drops-132881},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.47},
  annote =	{Keywords: Updatable timed automata, Reachability, Zones, Simulations, Static analysis}
}
Document
Reachability in Timed Automata with Diagonal Constraints

Authors: Paul Gastin, Sayan Mukherjee, and B. Srivathsan

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)


Abstract
We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test Z <= Z' which ascertains that zone Z does not reach more states than zone Z', and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. We propose a simulation relation <=_{LU}^d for timed automata with diagonal constraints. On the negative side, we show that deciding Z not <=_{LU}^d Z' is NP-complete. On the positive side, we identify a witness for Z not <=_{LU}^d Z' and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice.

Cite as

Paul Gastin, Sayan Mukherjee, and B. Srivathsan. Reachability in Timed Automata with Diagonal Constraints. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gastin_et_al:LIPIcs.CONCUR.2018.28,
  author =	{Gastin, Paul and Mukherjee, Sayan and Srivathsan, B.},
  title =	{{Reachability in Timed Automata with Diagonal Constraints}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.28},
  URN =		{urn:nbn:de:0030-drops-95660},
  doi =		{10.4230/LIPIcs.CONCUR.2018.28},
  annote =	{Keywords: Timed Automata, Reachability, Zones, Diagonal constraints}
}
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