20 Search Results for "Ravi, S. S."


Document
Online Paging with Heterogeneous Cache Slots

Authors: Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
It is natural to generalize the online k-Server problem by allowing each request to specify not only a point p, but also a subset S of servers that may serve it. To initiate a systematic study of this generalization, we focus on uniform and star metrics. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a page p, but also a subset S of cache slots, and is satisfied by having a copy of p in some slot in S. We call this problem Slot-Heterogenous Paging. In realistic settings only certain subsets of cache slots or servers would appear in requests. Therefore we parameterize the problem by specifying a family 𝒮 ⊆ 2^[k] of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache size k and family 𝒮. If all request sets are allowed (𝒮 = 2^[k]), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard Paging (𝒮 = {[k]}). As a function of |𝒮| and k, the optimal deterministic ratio is polynomial: at most O(k²|𝒮|) and at least Ω(√{|𝒮|}). For any laminar family {𝒮} of height h, the optimal ratios are O(hk) (deterministic) and O(h²log k) (randomized). The special case that we call All-or-One Paging extends standard Paging by allowing each request to specify a specific slot to put the requested page in. For All-or-One Paging the optimal competitive ratios are Θ(k) (deterministic) and Θ(log k) (randomized), while the offline problem is NP-hard. We extend the deterministic upper bound to the weighted variant of All-or-One Paging (a generalization of standard Weighted Paging), showing that it is also Θ(k). Some results for the laminar case are shown via a reduction to the generalization of Paging in which each request specifies a set P of pages, and is satisfied by fetching any page from P into the cache. The optimal ratios for the latter problem (with laminar family of height h) are at most hk (deterministic) and hH_k (randomized).

Cite as

Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young. Online Paging with Heterogeneous Cache Slots. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chrobak_et_al:LIPIcs.STACS.2023.23,
  author =	{Chrobak, Marek and Haney, Samuel and Liaee, Mehraneh and Panigrahi, Debmalya and Rajaraman, Rajmohan and Sundaram, Ravi and Young, Neal E.},
  title =	{{Online Paging with Heterogeneous Cache Slots}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.23},
  URN =		{urn:nbn:de:0030-drops-176759},
  doi =		{10.4230/LIPIcs.STACS.2023.23},
  annote =	{Keywords: Caching and paging algorithms, k-server, weighted paging, laminar family}
}
Document
Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH

Authors: Akanksha Agrawal, Ravi Kiran Allumalla, and Varun Teja Dhanekula

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
In this article we study a well-known problem, called Bipartite Token Jumping and not-so-well known problem(s), which we call, Half (Induced-) Subgraph, and show that under Gap-ETH, these problems do not admit FPT algorithms. The problem Bipartite Token Jumping takes as input a bipartite graph G and two independent sets S,T in G, where |S| = |T| = k, and the objective is to test if there is a sequence of exactly k-sized independent sets ⟨ I₀, I₁,⋯, I_𝓁 ⟩ in G, such that: i) I₀ = S and I_𝓁 = T, and ii) for every j ∈ [𝓁], I_{j} is obtained from I_{j-1} by replacing a vertex in I_{j-1} by a vertex in V(G) ⧵ I_{j-1}. We show that, assuming Gap-ETH, Bipartite Token Jumping does not admit an FPT algorithm. We note that this result resolves one of the (two) open problems posed by Bartier et al. (ISAAC 2020), under Gap-ETH. Most of the known reductions related to Token Jumping exploit the property given by triangles (i.e., C₃s), to obtain the correctness, and our results refutes FPT algorithm for Bipartite Token Jumping, where the input graph cannot have any triangles. For an integer k ∈ ℕ, the half graph S_{k,k} is the graph with vertex set V(S_{k,k}) = A_k ∪ B_k, where A_k = {a₁,a₂,⋯, a_k} and B_k = {b₁,b₂,⋯, b_k}, and for i,j ∈ [k], {a_i,b_j} ∈ E(T_{k,k}) if and only if j ≥ i. We also study the Half (Induced-)Subgraph problem where we are given a graph G and an integer k, and the goal is to check if G contains S_{k,k} as an (induced-)subgraph. Again under Gap-ETH, we show that Half (Induced-)Subgraph does not admit an FPT algorithm, even when the input is a bipartite graph. We believe that the above problem (and its negative) result maybe of independent interest and could be useful obtaining new fixed parameter intractability results. There are very few reductions known in the literature which refute FPT algorithms for a parameterized problem based on assumptions like Gap-ETH. Thus our technique (and simple reductions) exhibits the potential of such conjectures in obtaining new (and possibly easier) proofs for refuting FPT algorithms for parameterized problems.

Cite as

Akanksha Agrawal, Ravi Kiran Allumalla, and Varun Teja Dhanekula. Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2021.2,
  author =	{Agrawal, Akanksha and Allumalla, Ravi Kiran and Dhanekula, Varun Teja},
  title =	{{Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.2},
  URN =		{urn:nbn:de:0030-drops-153851},
  doi =		{10.4230/LIPIcs.IPEC.2021.2},
  annote =	{Keywords: Token Jumping, Bipartite Graphs, Fixed Parameter Intractability, Half Graphs, Gap-Exponential Time Hypothesis}
}
Document
Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing

Authors: Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu

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


Abstract
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.

Cite as

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-dev.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}
}
Document
Quantum-Inspired Algorithms for Solving Low-Rank Linear Equation Systems with Logarithmic Dependence on the Dimension

Authors: Nai-Hui Chia, András Gilyén, Han-Hsuan Lin, Seth Lloyd, Ewin Tang, and Chunhao Wang

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)


Abstract
We present two efficient classical analogues of the quantum matrix inversion algorithm [Harrow et al., 2009] for low-rank matrices. Inspired by recent work of Tang [Tang, 2019], assuming length-square sampling access to input data, we implement the pseudoinverse of a low-rank matrix allowing us to sample from the solution to the problem Ax = b using fast sampling techniques. We construct implicit descriptions of the pseudo-inverse by finding approximate singular value decomposition of A via subsampling, then inverting the singular values. In principle, our approaches can also be used to apply any desired "smooth" function to the singular values. Since many quantum algorithms can be expressed as a singular value transformation problem [András Gilyén et al., 2019], our results indicate that more low-rank quantum algorithms can be effectively "dequantised" into classical length-square sampling algorithms.

Cite as

Nai-Hui Chia, András Gilyén, Han-Hsuan Lin, Seth Lloyd, Ewin Tang, and Chunhao Wang. Quantum-Inspired Algorithms for Solving Low-Rank Linear Equation Systems with Logarithmic Dependence on the Dimension. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{chia_et_al:LIPIcs.ISAAC.2020.47,
  author =	{Chia, Nai-Hui and Gily\'{e}n, Andr\'{a}s and Lin, Han-Hsuan and Lloyd, Seth and Tang, Ewin and Wang, Chunhao},
  title =	{{Quantum-Inspired Algorithms for Solving Low-Rank Linear Equation Systems with Logarithmic Dependence on the Dimension}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.47},
  URN =		{urn:nbn:de:0030-drops-133916},
  doi =		{10.4230/LIPIcs.ISAAC.2020.47},
  annote =	{Keywords: sublinear algorithms, quantum-inspired, regression, importance sampling, quantum machine learning}
}
Document
Vertex Downgrading to Minimize Connectivity

Authors: Hassene Aissi, Da Qi Chen, and R. Ravi

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


Abstract
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.

Cite as

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-dev.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}
}
Document
Primal-Dual 2-Approximation Algorithm for the Monotonic Multiple Depot Heterogeneous Traveling Salesman Problem

Authors: S. Rathinam, R. Ravi, J. Bae, and K. Sundar

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


Abstract
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.

Cite as

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-dev.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}
}
Document
APPROX
Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty

Authors: David Ellis Hershkowitz, R. Ravi, and Sahil Singla

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


Abstract
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.

Cite as

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-dev.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}
}
Document
Multicommodity Multicast, Wireless and Fast

Authors: R. Ravi and Oleksandr Rudenko

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


Abstract
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.

Cite as

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-dev.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}
}
Document
New Bounds for Range Closest-Pair Problems

Authors: Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)


Abstract
Given a dataset S of points in R^2, the range closest-pair (RCP) problem aims to preprocess S into a data structure such that when a query range X is specified, the closest-pair in S cap X can be reported efficiently. The RCP problem can be viewed as a range-search version of the classical closest-pair problem, and finds applications in many areas. Due to its non-decomposability, the RCP problem is much more challenging than many traditional range-search problems. This paper revisits the RCP problem, and proposes new data structures for various query types including quadrants, strips, rectangles, and halfplanes. Both worst-case and average-case analyses (in the sense that the data points are drawn uniformly and independently from the unit square) are applied to these new data structures, which result in new bounds for the RCP problem. Some of the new bounds significantly improve the previous results, while the others are entirely new.

Cite as

Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan. New Bounds for Range Closest-Pair Problems. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{xue_et_al:LIPIcs.SoCG.2018.73,
  author =	{Xue, Jie and Li, Yuan and Rahul, Saladi and Janardan, Ravi},
  title =	{{New Bounds for Range Closest-Pair Problems}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{73:1--73:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.73},
  URN =		{urn:nbn:de:0030-drops-87865},
  doi =		{10.4230/LIPIcs.SoCG.2018.73},
  annote =	{Keywords: Closest-pair, Range search, Candidate pairs, Average-case analysis}
}
Document
Symmetric Interdiction for Matching Problems

Authors: Samuel Haney, Bruce Maggs, Biswaroop Maiti, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram

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


Abstract
Motivated by denial-of-service network attacks, we introduce the symmetric interdiction model, where both the interdictor and the optimizer are subject to the same constraints of the underlying optimization problem. We give a general framework that relates optimization to symmetric interdiction for a broad class of optimization problems. We then study the symmetric matching interdiction problem - with applications in traffic engineering - in more detail. This problem can be simply stated as follows: find a matching whose removal minimizes the size of the maximum matching in the remaining graph. We show that this problem is APX-hard, and obtain a 3/2-approximation algorithm that improves on the approximation guarantee provided by the general framework.

Cite as

Samuel Haney, Bruce Maggs, Biswaroop Maiti, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram. Symmetric Interdiction for Matching Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{haney_et_al:LIPIcs.APPROX-RANDOM.2017.9,
  author =	{Haney, Samuel and Maggs, Bruce and Maiti, Biswaroop and Panigrahi, Debmalya and Rajaraman, Rajmohan and Sundaram, Ravi},
  title =	{{Symmetric Interdiction for Matching Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{9:1--9:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.9},
  URN =		{urn:nbn:de:0030-drops-75587},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.9},
  annote =	{Keywords: Approximation algorithms, matching, interdiction Digital Object}
}
Document
On the Integrality Gap of the Prize-Collecting Steiner Forest LP

Authors: Jochen Könemann, Neil Olver, Kanstantsin Pashkovich, R. Ravi, Chaitanya Swamy, and Jens Vygen

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


Abstract
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.

Cite as

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-dev.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}
}
Document
The Multi-Domain Frame Packing Problem for CAN-FD

Authors: Prachi Joshi, Haibo Zeng, Unmesh D. Bordoloi, Soheil Samii, S. S. Ravi, and Sandeep K. Shukla

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


Abstract
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).

Cite as

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-dev.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
On the Separability of Stochastic Geometric Objects, with Applications

Authors: Jie Xue, Yuan Li, and Ravi Janardan

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)


Abstract
In this paper, we study the linear separability problem for stochastic geometric objects under the well-known unipoint/multipoint uncertainty models. Let S=S_R U S_B be a given set of stochastic bichromatic points, and define n = min{|S_R|, |S_B|} and N = max{|S_R|, |S_B|}. We show that the separable-probability (SP) of S can be computed in O(nN^{d-1}) time for d >= 3 and O(min{nN log N, N^2}) time for d=2, while the expected separation-margin (ESM) of S can be computed in O(nN^d) time for d >= 2. In addition, we give an Omega(nN^{d-1}) witness-based lower bound for computing SP, which implies the optimality of our algorithm among all those in this category. Also, a hardness result for computing ESM is given to show the difficulty of further improving our algorithm. As an extension, we generalize the same problems from points to general geometric objects, i.e., polytopes and/or balls, and extend our algorithms to solve the generalized SP and ESM problems in O(nN^d) and O(nN^{d+1}) time, respectively. Finally, we present some applications of our algorithms to stochastic convex-hull related problems.

Cite as

Jie Xue, Yuan Li, and Ravi Janardan. On the Separability of Stochastic Geometric Objects, with Applications. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 62:1-62:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{xue_et_al:LIPIcs.SoCG.2016.62,
  author =	{Xue, Jie and Li, Yuan and Janardan, Ravi},
  title =	{{On the Separability of Stochastic Geometric Objects, with Applications}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{62:1--62:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.62},
  URN =		{urn:nbn:de:0030-drops-59544},
  doi =		{10.4230/LIPIcs.SoCG.2016.62},
  annote =	{Keywords: Stochastic objects, linear separability, separable-probability, expected separation-margin, convex hull}
}
Document
10141 Abstracts Collection – Distributed Usage Control

Authors: Sandro Etalle, Alexander Pretschner, Ravi S. Sandhu, and Marianne Winslett

Published in: Dagstuhl Seminar Proceedings, Volume 10141, Distributed Usage Control (2010)


Abstract
From 06.04. to 09.04.2010, the Dagstuhl Seminar 10141 ``Distributed Usage Control '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Sandro Etalle, Alexander Pretschner, Ravi S. Sandhu, and Marianne Winslett. 10141 Abstracts Collection – Distributed Usage Control. In Distributed Usage Control. Dagstuhl Seminar Proceedings, Volume 10141, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{etalle_et_al:DagSemProc.10141.1,
  author =	{Etalle, Sandro and Pretschner, Alexander and Sandhu, Ravi S. and Winslett, Marianne},
  title =	{{10141 Abstracts Collection – Distributed Usage Control}},
  booktitle =	{Distributed Usage Control},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10141},
  editor =	{Sandro Etalle and Alexander Pretschner and Raiv S. Sandhu and Marianne Winslett},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10141.1},
  URN =		{urn:nbn:de:0030-drops-27185},
  doi =		{10.4230/DagSemProc.10141.1},
  annote =	{Keywords: Usage control, access control, data protection, privacy, security policies, trust, trusted computing, compliance, DRM, information flow}
}
Document
10141 Summary – Distributed Usage Control

Authors: Sandro Etalle, Alexander Pretschner, Ravi S. Sandhu, and Marianne Winslett

Published in: Dagstuhl Seminar Proceedings, Volume 10141, Distributed Usage Control (2010)


Abstract
We summarize Dagstuhl seminar 10141 on Distributed Usage Control.

Cite as

Sandro Etalle, Alexander Pretschner, Ravi S. Sandhu, and Marianne Winslett. 10141 Summary – Distributed Usage Control. In Distributed Usage Control. Dagstuhl Seminar Proceedings, Volume 10141, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{etalle_et_al:DagSemProc.10141.2,
  author =	{Etalle, Sandro and Pretschner, Alexander and Sandhu, Ravi S. and Winslett, Marianne},
  title =	{{10141 Summary – Distributed Usage Control}},
  booktitle =	{Distributed Usage Control},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10141},
  editor =	{Sandro Etalle and Alexander Pretschner and Raiv S. Sandhu and Marianne Winslett},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10141.2},
  URN =		{urn:nbn:de:0030-drops-27174},
  doi =		{10.4230/DagSemProc.10141.2},
  annote =	{Keywords: Usage control, access control, data protection, privacy, security policies, trust, trusted computing, compliance, DRM, information flow}
}
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