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**Published in:** LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data. Instance robustness ensures that the prediction is robust to modest changes in the problem input, where the measure of the change may be problem specific. Instance robustness insists on a smooth degradation in performance as a function of the change. Ideally, the performance is never worse than worst-case bounds. This also allows predictions to be objectively compared.
We design online algorithms with predictions for a network flow allocation problem and restricted assignment makespan minimization. For both problems, two key properties are established: high quality predictions can be learned from a small sample of prior instances and these predictions are robust to errors that smoothly degrade as the underlying problem instance changes.

Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu. Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lavastida_et_al:LIPIcs.ESA.2021.59, author = {Lavastida, Thomas and Moseley, Benjamin and Ravi, R. and Xu, Chenyang}, title = {{Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing}}, booktitle = {29th Annual European Symposium on Algorithms (ESA 2021)}, pages = {59:1--59:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-204-4}, ISSN = {1868-8969}, year = {2021}, volume = {204}, editor = {Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.59}, URN = {urn:nbn:de:0030-drops-146405}, doi = {10.4230/LIPIcs.ESA.2021.59}, annote = {Keywords: Learning-augmented algorithms, Online algorithms, Flow allocation} }

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**Published in:** LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria (4,4)-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. We accomplish this with an LP relaxation and rounding using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of k levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get a (4k,4k)-approximation for this case.

Hassene Aissi, Da Qi Chen, and R. Ravi. Vertex Downgrading to Minimize Connectivity. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aissi_et_al:LIPIcs.SWAT.2020.5, author = {Aissi, Hassene and Chen, Da Qi and Ravi, R.}, title = {{Vertex Downgrading to Minimize Connectivity}}, booktitle = {17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)}, pages = {5:1--5:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-150-4}, ISSN = {1868-8969}, year = {2020}, volume = {162}, editor = {Albers, Susanne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.5}, URN = {urn:nbn:de:0030-drops-122527}, doi = {10.4230/LIPIcs.SWAT.2020.5}, annote = {Keywords: Vertex Interdiction, Vertex Downgrading, Network Interdiction, Approximation Algorithm} }

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**Published in:** LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

We study a Multiple Depot Heterogeneous Traveling Salesman Problem (MDHTSP) where the cost of the traveling between any two targets depends on the type of the vehicle. The travel costs are assumed to be symmetric, satisfy the triangle inequality, and are monotonic, i.e., the travel costs between any two targets monotonically increases with the index of the vehicles. Exploiting the monotonic structure of the travel costs, we present a 2-approximation algorithm based on the primal-dual method.

S. Rathinam, R. Ravi, J. Bae, and K. Sundar. Primal-Dual 2-Approximation Algorithm for the Monotonic Multiple Depot Heterogeneous Traveling Salesman Problem. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 33:1-33:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rathinam_et_al:LIPIcs.SWAT.2020.33, author = {Rathinam, S. and Ravi, R. and Bae, J. and Sundar, K.}, title = {{Primal-Dual 2-Approximation Algorithm for the Monotonic Multiple Depot Heterogeneous Traveling Salesman Problem}}, booktitle = {17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)}, pages = {33:1--33:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-150-4}, ISSN = {1868-8969}, year = {2020}, volume = {162}, editor = {Albers, Susanne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.33}, URN = {urn:nbn:de:0030-drops-122805}, doi = {10.4230/LIPIcs.SWAT.2020.33}, annote = {Keywords: Approximation Algorithm, Heterogeneous Traveling Salesman Problem, Primal-dual Method} }

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APPROX

**Published in:** LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may build rigid resources that cannot be changed for different scenarios. Once we know which scenarios appear, we are allowed to rent reconfigurable but expensive resources to use across scenarios. Although computing the objective in our model might seem to require enumerating exponentially-many possibilities, we show it is well estimated by a surrogate objective which is representable by a polynomial-size LP. In this surrogate objective we pay for each scenario only to the extent that it exceeds a certain threshold. Using this objective we design algorithms that approximately-optimally balance inflexible and reconfigurable resources for several NP-hard covering problems. For example, we study variants of minimum spanning and Steiner trees, minimum cuts, and facility location. Up to constants, our approximation guarantees match those of previously-studied algorithms for demand-robust and stochastic two-stage models. Lastly, we demonstrate that our problem is sufficiently general to smoothly interpolate between previous demand-robust and stochastic two-stage problems.

David Ellis Hershkowitz, R. Ravi, and Sahil Singla. Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hershkowitz_et_al:LIPIcs.APPROX-RANDOM.2019.4, author = {Hershkowitz, David Ellis and Ravi, R. and Singla, Sahil}, title = {{Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)}, pages = {4:1--4:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-125-2}, ISSN = {1868-8969}, year = {2019}, volume = {145}, editor = {Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.4}, URN = {urn:nbn:de:0030-drops-112196}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.4}, annote = {Keywords: Approximation Algorithms, Optimization Under Uncertainty, Two-Stage Optimization, Expected Max} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

We study rumor spreading in graphs, specifically multicommodity multicast problem under the wireless model: given source-destination pairs in the graph, one needs to find the fastest schedule to transfer information from each source to the corresponding destination. Under the wireless model, nodes can transmit to any subset of their neighbors in synchronous time steps, as long as they either transmit or receive from at most one transmitter during the same time step. We improve approximation ratio for this problem from O~(n^(2/3)) to O~(n^((1/2) + epsilon)) on n-node graphs. We also design an algorithm that satisfies p given demand pairs in O(OPT + p) steps, where OPT is the length of an optimal schedule, by reducing it to the well-studied packet routing problem. In the case where underlying graph is an n-node tree, we improve the previously best-known approximation ratio of O((log n)/(log log n)) to 3. One consequence of our proof is a simple constructive rule for optimal broadcasting in a tree under a widely studied telephone model.

R. Ravi and Oleksandr Rudenko. Multicommodity Multicast, Wireless and Fast. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ravi_et_al:LIPIcs.ESA.2019.78, author = {Ravi, R. and Rudenko, Oleksandr}, title = {{Multicommodity Multicast, Wireless and Fast}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {78:1--78:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.78}, URN = {urn:nbn:de:0030-drops-111991}, doi = {10.4230/LIPIcs.ESA.2019.78}, annote = {Keywords: Rumor, scheduling, broadcast, multicommodity, multicast, optimization algorithms, approximation, packet routing} }

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**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

We show that Karger's randomized contraction method (SODA 93) can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient algorithms.
For global minimum cuts with a single edge-budget constraint, our extension of the randomized contraction method has running time tilde{O}(n^3) in an n-node graph improving upon the best-known randomized algorithm with running time tilde{O}(n^4) due to Armon and Zwick (Algorithmica 2006). Our analysis also gives a new upper bound of O(n^3) for the number of optimal solutions for a single edge-budget min cut problem. For the case of (k-1) edge-budget constraints, the extension of our algorithm saves a logarithmic factor from the best-known randomized running time of O(n^{2k} log^3 n). A main feature of our algorithms is to adaptively choose, at each step, the appropriate cost function used in the random selection of edges to be contracted.
For the global min cut problem with a constant number of node budgets, we give a randomized algorithm with running time tilde{O}(n^2), improving the current best determinisitic running time of O(n^3) due to Goemans and Soto (SIAM Journal on Discrete Mathematics 2013). Our method also shows that the total number of distinct optimal solutions is bounded by O(n^2) as in the case of global min-cuts. Our algorithm extends to the node-budget constrained global min cut problem excluding a given sink with the same running time and bound on number of optimal solutions, again improving upon the best-known running time by a factor of O(n). For node-budget constrained problems, our improvements arise from incorporating the idea of merging any infeasible super-nodes that arise during the random contraction process.
In contrast to cuts excluding a sink, we note that the node-cardinality constrained min-cut problem containing a given source is strongly NP-hard using a reduction from graph bisection.

Hassene Aissi, Ali Ridha Mahjoub, and R. Ravi. Randomized Contractions for Multiobjective Minimum Cuts. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aissi_et_al:LIPIcs.ESA.2017.6, author = {Aissi, Hassene and Mahjoub, Ali Ridha and Ravi, R.}, title = {{Randomized Contractions for Multiobjective Minimum Cuts}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {6:1--6:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.6}, URN = {urn:nbn:de:0030-drops-78686}, doi = {10.4230/LIPIcs.ESA.2017.6}, annote = {Keywords: minimum cut, multiobjective optimization, budget constraints, graph algorithms, randomized algorithms} }

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**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

We study a generalization of the Steiner tree problem, where we are given a weighted network G together with a collection of k subsets of its vertices and a root r. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultaneously.
We settle an open question regarding the complexity of this problem for k=2, and give a 3/2-approximation algorithm that improves over a (trivial) known 2-approximation. Furthermore, we prove some structural results that prevent many well-known techniques from doing better than the known O(log n)-approximation. Despite these obstacles, we conjecture that this problem should have an O(1)-approximation. We also give an approximation result for a variant of the problem where the solution is required to be a path.

Guru Guruganesh, Jennifer Iglesias, R. Ravi, and Laura Sanita. Single-Sink Fractionally Subadditive Network Design. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guruganesh_et_al:LIPIcs.ESA.2017.46, author = {Guruganesh, Guru and Iglesias, Jennifer and Ravi, R. and Sanita, Laura}, title = {{Single-Sink Fractionally Subadditive Network Design}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {46:1--46:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.46}, URN = {urn:nbn:de:0030-drops-78581}, doi = {10.4230/LIPIcs.ESA.2017.46}, annote = {Keywords: Network design, single-commodity flow, approximation algorithms, Steiner tree} }

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**Published in:** LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph G=(V,E), nonnegative edge costs {c_e} for e in E, terminal pairs {(s_i,t_i)} for i=1,...,k, and penalties {pi_i} for i=1,...,k for each terminal pair; the goal is to find a forest F to minimize c(F) + sum{ pi_i: (s_i,t_i) is not connected in F }. The Steiner forest problem can be viewed as the special case where pi_i are infinite for all i. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF (PCSF-LP) is at most 2. We dispel this belief by showing that the integrality gap of this LP is at least 9/4 even if the input instance is planar. We also show that using this LP, one cannot devise a Lagrangian-multiplier-preserving (LMP) algorithm with approximation guarantee better than 4. Our results thus show a separation between the integrality gaps of the LP-relaxations for prize-collecting and non-prize-collecting (i.e., standard) Steiner forest, as well as the approximation ratios achievable relative to the optimal LP solution by LMP- and non-LMP-approximation algorithms for PCSF. For the special case of prize-collecting Steiner tree (PCST), we prove that the natural LP relaxation admits basic feasible solutions with all coordinates of value at most 1/3 and all edge variables positive. Thus, we rule out the possibility of approximating PCST with guarantee better than 3 using a direct iterative rounding method.

Jochen Könemann, Neil Olver, Kanstantsin Pashkovich, R. Ravi, Chaitanya Swamy, and Jens Vygen. On the Integrality Gap of the Prize-Collecting Steiner Forest LP. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{konemann_et_al:LIPIcs.APPROX-RANDOM.2017.17, author = {K\"{o}nemann, Jochen and Olver, Neil and Pashkovich, Kanstantsin and Ravi, R. and Swamy, Chaitanya and Vygen, Jens}, title = {{On the Integrality Gap of the Prize-Collecting Steiner Forest LP}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)}, pages = {17:1--17:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-044-6}, ISSN = {1868-8969}, year = {2017}, volume = {81}, editor = {Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.17}, URN = {urn:nbn:de:0030-drops-75665}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.17}, annote = {Keywords: Integrality gap, Steiner tree, Steiner forest, prize-collecting, Lagrangianmultiplier- preserving} }

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**Published in:** LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

We study the problem of computing a minimum time schedule to spread rumors in a given graph under several models: In the radio model, all neighbors of a transmitting node listen to the messages and are able to record it only when no other neighbor is transmitting; In the wireless model (also called the edge-star model), each transmitter is at a different frequency to which any neighbor can tune to, but only one neighboring transmission can be accessed in this way; In the telephone model, the set of transmitter-receiver pairs form a matching in the graph. The rumor spreading problems assume a message at one or several nodes of the graph that must reach a target node or set of nodes. The transmission proceeds in synchronous rounds under the rules of the corresponding model. The goal is to compute a schedule that completes in the minimum number of rounds.
We present a comprehensive study of approximation algorithms for these problems, and show several reductions from the harder to the easier models for special demands. We show a new hardness of approximation of Omega(n^1/2 - epsilon) for the minimum radio gossip time by a connection to maximum induced matchings. We give the first sublinear approximation algorithms for the most general case of the problem under the wireless model; we also consider various special cases such as instances with symmetric demands and give better approximation algorithms. Our work exposes the relationships across the models and opens up several new avenues for further study.

Jennifer Iglesias, Rajmohan Rajaraman, R. Ravi, and Ravi Sundaram. Rumors Across Radio, Wireless, Telephone. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 517-528, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{iglesias_et_al:LIPIcs.FSTTCS.2015.517, author = {Iglesias, Jennifer and Rajaraman, Rajmohan and Ravi, R. and Sundaram, Ravi}, title = {{Rumors Across Radio, Wireless, Telephone}}, booktitle = {35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)}, pages = {517--528}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-97-2}, ISSN = {1868-8969}, year = {2015}, volume = {45}, editor = {Harsha, Prahladh and Ramalingam, G.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.517}, URN = {urn:nbn:de:0030-drops-56383}, doi = {10.4230/LIPIcs.FSTTCS.2015.517}, annote = {Keywords: Broadcast, Gossip, Approximation algorithms, Graph algorithms, Hardness of Approximation} }

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**Published in:** LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

From the publish-subscribe systems of the early days of the Internet to the recent emergence of Web 3.0 and IoT (Internet of Things), new problems arise in the design of networks centered at producers and consumers of constantly evolving information. In a typical problem, each terminal is a source or sink of information and builds a physical network in the form of a tree or an overlay network in the form of a star rooted at itself. Every pair of pub-sub terminals that need to be coordinated (e.g. the source and sink of an important piece of control information) define an edge in a bipartite demand graph; the solution must ensure that the corresponding networks rooted at the endpoints of each demand edge overlap at some node. This simple overlap constraint, and the requirement that each network is a tree or a star, leads to a variety of new questions on the design of overlapping networks.
In this paper, for the general demand case of the problem, we show that a natural LP formulation has a non-constant integrality gap; on the positive side, we present a logarithmic approximation for the general demand case. When the demand graph is complete, however, we design approximation algorithms with small constant performance ratios, irrespective of whether the pub networks and sub networks are required to be trees or stars.

Jennifer Iglesias, Rajmohan Rajaraman, R. Ravi, and Ravi Sundaram. Designing Overlapping Networks for Publish-Subscribe Systems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 381-395, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{iglesias_et_al:LIPIcs.APPROX-RANDOM.2015.381, author = {Iglesias, Jennifer and Rajaraman, Rajmohan and Ravi, R. and Sundaram, Ravi}, title = {{Designing Overlapping Networks for Publish-Subscribe Systems}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)}, pages = {381--395}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-89-7}, ISSN = {1868-8969}, year = {2015}, volume = {40}, editor = {Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.381}, URN = {urn:nbn:de:0030-drops-53133}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2015.381}, annote = {Keywords: Approximation Algorithms, Steiner Trees, Publish-Subscribe Systems, Integrality Gap, VPN.} }

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**Published in:** LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

The inventory routing problem involves trading off inventory holding
costs at client locations with vehicle routing costs to deliver
frequently from a single central depot to meet deterministic client demands over a finite planing horizon. In this paper, we consider periodic solutions that visit clients in one of several specified frequencies, and focus on the case when the frequencies of visiting nodes are nested. We give the first constant-factor approximation algorithms for designing optimum nested periodic schedules for the problem with no limit on vehicle capacities by simple reductions to prize-collecting network design problems. For instance, we present a 2.55-approximation algorithm for the minimum-cost nested periodic
schedule where the vehicle routes are modeled as minimum Steiner trees. We also show a general reduction from the capacitated
problem where all vehicles have the same capacity to the uncapacitated
version with a slight loss in performance. This reduction gives a
4.55-approximation for the capacitated problem. In addition, we prove several structural results relating the values of optimal policies of various types.

Takuro Fukunaga, Afshin Nikzad, and R. Ravi. Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 209-225, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{fukunaga_et_al:LIPIcs.APPROX-RANDOM.2014.209, author = {Fukunaga, Takuro and Nikzad, Afshin and Ravi, R.}, title = {{Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)}, pages = {209--225}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-74-3}, ISSN = {1868-8969}, year = {2014}, volume = {28}, editor = {Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.209}, URN = {urn:nbn:de:0030-drops-46985}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.209}, annote = {Keywords: Inventry Routing Problem, Approximation algorithm, Prize-collecting Steiner Tree} }

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**Published in:** LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time 9/7-approximation algorithm for cubic bipartite graphs and a (9/7+1/(21(k-2)))-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are able to do by leveraging the fact that all cycles in bipartite graphs are of even length along with our knowledge of the structure of cubic graphs.

Jeremy A. Karp and R. Ravi. A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 284-296, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{karp_et_al:LIPIcs.APPROX-RANDOM.2014.284, author = {Karp, Jeremy A. and Ravi, R.}, title = {{A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)}, pages = {284--296}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-74-3}, ISSN = {1868-8969}, year = {2014}, volume = {28}, editor = {Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.284}, URN = {urn:nbn:de:0030-drops-47034}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.284}, annote = {Keywords: Approximation algorithms, traveling salesman problem, Barnette’s conjecture, combinatorial optimization} }

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Invited Talk

**Published in:** LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

In these lectures, I will describe a simple iterative method that supplies new proofs of integrality of linear characterizations of various basic problems in combinatorial optimization, and also allows adaptations to design approximation algorithms for NP-hard variants of these problems involving extra "degree-like" budget constraints. It is inspired by Jain's iterative rounding method for designing approximation algorithms for survivable network design problems, and augmented with a relaxation idea in the work of Lau, Naor, Salvatipour and Singh in their work on designing the approximation algorithm for its degree bounded version. Its application was further refined in recent work of Bansal, Khandekar and Nagarajan on degree-bounded directed network design.
I will begin by reviewing the background material on LP relaxations and their solvability and properties of extreme point or vertex solutions to such problems. I will then introduce the basic framework of the method using the assignment problem, and show its application by re-deriving the approximation results of Shmoys and Tardos for the generalized assignment problem.
I will then discuss linear characterizations for the spanning tree polyhedron in undirected graphs and give a new proof of integrality using an iterative method. I will then illustrate an application to approximating the degree-bounded version of the undirected problem, by proving the results of Goemans and Lau & Singh.
I will continue with showing how these methods for spanning trees simplify and generalize to showing linear descriptions of maximum weight matroid bases and also maximum weight sets that are independent in two different matroids. This also leads to good additive approximation algorithms for a bounded degree version of the matroid basis problem.
I will close with applications of the iterative method by revisiting Jain's original proof for the SNDP and giving a new proof that unifies its treatment with that for the Symmetric TSP polyhedron (describing joint work with Nagarajan and Singh). I will also outline the versatility of the method by pointing out the other problems for which the method has been applied, summarizing the discussion in a recent monograph I have co-authored on this topic with Lap Chi Lau and Mohit Singh (published by Cambridge University Press, 2011).

R. Ravi. Iterative Methods in Combinatorial Optimization (Invited Talk). In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, p. 24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{ravi:LIPIcs.STACS.2012.24, author = {Ravi, R.}, title = {{Iterative Methods in Combinatorial Optimization}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {24--24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-35-4}, ISSN = {1868-8969}, year = {2012}, volume = {14}, editor = {D\"{u}rr, Christoph and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.24}, URN = {urn:nbn:de:0030-drops-33876}, doi = {10.4230/LIPIcs.STACS.2012.24}, annote = {Keywords: combinatorial optimization, linear programming, matroid} }

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**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We describe a simple iterative method for proving a variety of results in combinatorial optimization. It is inspired by Jain's iterative rounding method (FOCS 1998) for designing approximation algorithms for survivable network design problems, and augmented with a relaxation idea in the work of Lau, Naor, Salvatipour and Singh (STOC 2007) on designing an approximation algorithm for its degree bounded version. At the heart of the method is a counting argument that redistributes tokens from the columns to the rows of an LP extreme point. This token argument was further refined to
fractional assignment and redistribution in work of Bansal, Khandekar and Nagarajan on degree-bounded directed network design (STOC 2008). In this presentation, we introduce the method using the assignment problem, describe its application to showing the integrality of Edmond's characterization (1971) of the spanning tree polyhedron, and then extend the argument to show a simple proof of the Singh and Lau's approximation
algorithm (STOC 2007) for its degree constrained version, due to Bansal, Khandekar and Nagarajan. We conclude by showing how Jain's original proof can also be simplified by using a fractional token argument (joint work with
Nagarajan and Singh).
This presentation is extracted from an upcoming monograph on this topic
co-authored with Lau and Singh.

R. Ravi. Iterative Methods in Combinatorial Optimization. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 453-469, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{ravi:LIPIcs.FSTTCS.2009.2339, author = {Ravi, R.}, title = {{Iterative Methods in Combinatorial Optimization}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {453--469}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2339}, URN = {urn:nbn:de:0030-drops-23391}, doi = {10.4230/LIPIcs.FSTTCS.2009.2339}, annote = {Keywords: Iterative methods, combinatorial optimization, network design, approximation algorithms, assignment problem, linear programming} }

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**Published in:** LIPIcs, Volume 76, 29th Euromicro Conference on Real-Time Systems (ECRTS 2017)

The Controller Area Network with Flexible Data-Rate (CAN-FD) is a new communication protocol to meet the bandwidth requirements for the constantly growing volume of data exchanged in modern vehicles. The problem of frame packing for CAN-FD, as studied in the literature, assumes a single sub-system where one CAN-FD bus serves as the communication medium among several Electronic Control Units (ECUs). Modern automotive electronic systems, on the other hand, consist of several sub-systems, each facilitating a certain functional domain such as powertrain, chassis and suspension. A substantial fraction of all signals is exchanged across sub-systems. In this work, we study the frame packing problem for CAN-FD with multiple sub-systems, and propose a two-stage optimization framework. In the first stage, we pack the signals into frames with the objective of minimizing the bandwidth utilization. In the second stage, we extend Audsley's algorithm to assign priorities/identifiers to the frames. In case the resulting solution is not schedulable, our framework provides a potential repacking method. We propose two solution approaches: (a) an Integer Linear Programming (ILP) formulation that provides an optimal solution but is computationally expensive for industrial-size problems; and (b) a greedy heuristic that scales well and provides solutions that are comparable to optimal solutions. Experimental results show the efficiency of our optimization framework in achieving feasible solutions with low bandwidth utilization. The results also show a significant improvement over the case when there is no cross-domain consideration (as in prior work).

Prachi Joshi, Haibo Zeng, Unmesh D. Bordoloi, Soheil Samii, S. S. Ravi, and Sandeep K. Shukla. The Multi-Domain Frame Packing Problem for CAN-FD. In 29th Euromicro Conference on Real-Time Systems (ECRTS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 76, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{joshi_et_al:LIPIcs.ECRTS.2017.12, author = {Joshi, Prachi and Zeng, Haibo and Bordoloi, Unmesh D. and Samii, Soheil and Ravi, S. S. and Shukla, Sandeep K.}, title = {{The Multi-Domain Frame Packing Problem for CAN-FD}}, booktitle = {29th Euromicro Conference on Real-Time Systems (ECRTS 2017)}, pages = {12:1--12:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-037-8}, ISSN = {1868-8969}, year = {2017}, volume = {76}, editor = {Bertogna, Marko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2017.12}, URN = {urn:nbn:de:0030-drops-71551}, doi = {10.4230/LIPIcs.ECRTS.2017.12}, annote = {Keywords: Frame Packing, CAN-FD, Integer Linear Programming, Audsley's Algorithm} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 7041, Power-aware Computing Systems (2007)

Concurrent Action Oriented Specifications (CAOS) formalism such as Bluespec Inc.'s Bluespec System Verilog (BSV) has been recently shown to be effective for hardware modeling and synthesis. This formalism offers the benefits of automatic handling of concurrency issues in highly concurrent system descriptions, and the associated synthesis algorithms have been shown to produce efficient hardware comparable to those generated from hand-written Verilog/VHDL. These benefits which are inherent in such a synthesis process also aid in faster architectural exploration. This is because CAOS allows a high-level description (above RTL) of a design in terms of atomic transactions, where each transaction corresponds to a collection of operations. Optimal scheduling of such actions in CAOS-based synthesis process is crucial in order to generate hardware that is efficient in terms of area, latency and power. In this paper, we analyze the complexity of the scheduling problems associated
with CAOS-based synthesis and discuss several heuristics for meeting
the peak power goals of designs generated from CAOS. We also discuss
approximability of these problems as appropriate.

Gaurav Singh, S. S. Ravi, Sumit Ahuja, and Sandeep Shukla. Complexity of Scheduling in Synthesizing Hardware from Concurrent Action Oriented Specifications. In Power-aware Computing Systems. Dagstuhl Seminar Proceedings, Volume 7041, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{singh_et_al:DagSemProc.07041.6, author = {Singh, Gaurav and Ravi, S. S. and Ahuja, Sumit and Shukla, Sandeep}, title = {{Complexity of Scheduling in Synthesizing Hardware from Concurrent Action Oriented Specifications}}, booktitle = {Power-aware Computing Systems}, pages = {1--25}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {7041}, editor = {Luca Benini and Naehyuck Chang and Ulrich Kremer and Christian W. Probst}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07041.6}, URN = {urn:nbn:de:0030-drops-11055}, doi = {10.4230/DagSemProc.07041.6}, annote = {Keywords: Hardware Synthesis, Concurrent Action Oriented Specifications (CAOS), Scheduling, Complexity, Peak Power.} }

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**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

State-of-the-art software transactional memory (STM) implementations achieve good performance by carefully avoiding the overhead of incremental validation (i.e., re-reading previously read data items to avoid inconsistency) while still providing progressiveness (allowing transactional aborts only due to data conflicts). Hardware transactional memory (HTM) implementations promise even better performance, but offer no progress guarantees. Thus, they must be combined with STMs, leading to hybrid TMs (HyTMs) in which hardware transactions must be instrumented (i.e., access metadata) to detect contention with software transactions.
We show that, unlike in progressive STMs, software transactions in progressive HyTMs cannot avoid incremental validation. In fact, this result holds even if hardware transactions can read metadata non-speculatively. We then present opaque HyTM algorithms providing progressiveness for a subset of transactions that are optimal in terms of hardware instrumentation. We explore the concurrency vs. hardware instrumentation vs. software validation trade-offs for these algorithms. Our experiments with Intel and IBM POWER8 HTMs seem to suggest that (i) the cost of concurrency also exists in practice, (ii) it is important to implement HyTMs that provide progressiveness for a maximal set of transactions without incurring high hardware instrumentation overhead or using global contending bottlenecks and (iii) there is no easy way to derive more efficient HyTMs by taking advantage of non-speculative accesses within hardware.

Trevor Brown and Srivatsan Ravi. Cost of Concurrency in Hybrid Transactional Memory. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brown_et_al:LIPIcs.DISC.2017.9, author = {Brown, Trevor and Ravi, Srivatsan}, title = {{Cost of Concurrency in Hybrid Transactional Memory}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {9:1--9:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.9}, URN = {urn:nbn:de:0030-drops-79958}, doi = {10.4230/LIPIcs.DISC.2017.9}, annote = {Keywords: Transactional memory, Lower bounds, Opacity} }

Document

**Published in:** LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

The bottleneck-complexity (BC) of secure multiparty computation (MPC) protocols is a measure of the maximum number of bits which are sent and received by any party in protocol. As the name suggests, the goal of studying BC-efficient protocols is to increase overall efficiency by making sure that the workload in the protocol is somehow "amortized" by the protocol participants.
Orlandi et al. [Orlandi et al., 2022] initiated the study of BC-efficient protocols from simple assumptions in the correlated randomness model and for semi-honest adversaries. In this work, we extend the study of [Orlandi et al., 2022] in two primary directions: (a) to a larger and more general class of functions and (b) to the information-theoretic setting.
In particular, we offer semi-honest secure protocols for the useful function classes of abelian programs, "read-k" non-abelian programs, and "read-k" generalized formulas.
Our constructions use a novel abstraction, called incremental function secret-sharing (IFSS), that can be instantiated with unconditional security or from one-way functions (with different efficiency trade-offs).

Hannah Keller, Claudio Orlandi, Anat Paskin-Cherniavsky, and Divya Ravi. MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{keller_et_al:LIPIcs.ITC.2023.11, author = {Keller, Hannah and Orlandi, Claudio and Paskin-Cherniavsky, Anat and Ravi, Divya}, title = {{MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {11:1--11:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.11}, URN = {urn:nbn:de:0030-drops-183391}, doi = {10.4230/LIPIcs.ITC.2023.11}, annote = {Keywords: Secure Multiparty Computation, Bottleneck Complexity, Information-theoretic} }

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**Published in:** LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

In this paper, we explore the feasibility of reliable and private communication in dynamic networks, where in each round the adversary can choose which direct peer-to-peer links are available in the network graph, under the sole condition that the graph is k-connected at each round (for some k).
We show that reliable communication is possible in such a dynamic network if and only if k > 2t. We also show that if k = cn > 2 t for a constant c, we can achieve reliable communication with polynomial round and communication complexity.
For unconditionally private communication, we show that for a passive adversary, k > t is sufficient (and clearly necessary). For an active adversary, we show that k > 2t is sufficient for statistical security (and clearly necessary), while k > 3t is sufficient for perfect security. We conjecture that, in contrast to the static case, k > 2t is not enough for perfect security, and we give evidence that the conjecture is true.
Once we have reliable and private communication between each pair of parties, we can emulate a complete network with secure channels, and we can use known protocols to do secure computation.

Ivan Damgård, Divya Ravi, Daniel Tschudi, and Sophia Yakoubov. Secure Communication in Dynamic Incomplete Networks. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{damgard_et_al:LIPIcs.ITC.2023.13, author = {Damg\r{a}rd, Ivan and Ravi, Divya and Tschudi, Daniel and Yakoubov, Sophia}, title = {{Secure Communication in Dynamic Incomplete Networks}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {13:1--13:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.13}, URN = {urn:nbn:de:0030-drops-183419}, doi = {10.4230/LIPIcs.ITC.2023.13}, annote = {Keywords: Secure Communication, Dynamic Incomplete Network, Information-theoretic} }

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Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

We revisit the problem of distributed consensus in directed graphs tolerating crash failures; we improve the round and communication complexity of the existing protocols. Moreover, we prove that our protocol requires the optimal number of communication rounds, required by any protocol belonging to a specific class of crash-tolerant consensus protocols in directed graphs.

Ashish Choudhury, Gayathri Garimella, Arpita Patra, Divya Ravi, and Pratik Sarkar. Brief Announcement: Crash-Tolerant Consensus in Directed Graph Revisited. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 46:1-46:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{choudhury_et_al:LIPIcs.DISC.2017.46, author = {Choudhury, Ashish and Garimella, Gayathri and Patra, Arpita and Ravi, Divya and Sarkar, Pratik}, title = {{Brief Announcement: Crash-Tolerant Consensus in Directed Graph Revisited}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {46:1--46:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.46}, URN = {urn:nbn:de:0030-drops-79784}, doi = {10.4230/LIPIcs.DISC.2017.46}, annote = {Keywords: Directed graph, Consensus, Crash failure, Round complexity} }