Exact Distance Oracles for Planar Graphs with Failing Vertices

We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex $u$, a target vertex $v$ and a set $X$ of $k$ failed vertices, such an oracle returns the length of a shortest $u$-to-$v$ path that avoids all vertices in $X$. We propose oracles that can handle any number $k$ of failures. More specifically, for a directed weighted planar graph with $n$ vertices, any constant $k$, and for any $q \in [1,\sqrt n]$, we propose an oracle of size $\tilde{\mathcal{O}}(\frac{n^{k+3/2}}{q^{2k+1}})$ that answers queries in $\tilde{\mathcal{O}}(q)$ time. In particular, we show an $\tilde{\mathcal{O}}(n)$-size, $\tilde{\mathcal{O}}(\sqrt{n})$-query-time oracle for any constant $k$. This matches, up to polylogarithmic factors, the fastest failure-free distance oracles with nearly linear space. For single vertex failures ($k=1$), our $\tilde{\mathcal{O}}(\frac{n^{5/2}}{q^3})$-size, $\tilde{\mathcal{O}}(q)$-query-time oracle improves over the previously best known tradeoff of Baswana et al. [SODA 2012] by polynomial factors for $q = \Omega(n^t)$, $t \in (1/4,1/2]$. For multiple failures, no planarity exploiting results were previously known

Space Complexity of Two Adaptive Bitprobe Schemes Storing Three Elements

We consider the following set membership problem in the bitprobe model - that of storing subsets of size at most three from a universe of size m, and answering membership queries using two adaptive bitprobes. Baig and Kesh [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2018] proposed a scheme for the problem which takes O(m^{2/3}) space. In this paper, we present a proof which shows that any scheme for the problem requires Omega(m^{2/3}) amount of space. These two results together settle the space complexity issue for this particular problem

Algorithms - ESA 2010 : 18th annual European symposium, Liverpool, UK, September 6-8, 2010 : proceedings, part II

This volume contains the 69 papers presented at the 16th Annual European Symposium on Algorithms (ESA 2010), held in Liverpool during September 6–8, 2010, including three papers by the distinguished invited speakers Artur Czumaj, Herbert Edelsbrunner, and Paolo Ferragina. ESA 2010 was organized as a part of ALGO 2010, which also included the 10th Workshop on Algorithms in Bioinformatics (WABI), the 8th Workshop on Approximation and Online Algorithms (WAOA), and the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS). The European Symposium on Algorithms covers research in the design, use, and analysis of efficient algorithms and data structures. As in previous years, the symposium had two tracks: the Design and Analysis Track and the Engineering and Applications Track, each with its own Program Committee. In total 245 papers adhering to the submission guidelines were submitted. Each paper was reviewed by three or four referees. Based on the reviews and the often extensive electronic discussions following them, the committees selected 66 papers in total: 56 (out of 206) to the Design and Analysis Track and 10 (out of 39) to the Engineering and Applications track.We believe that these papers together made up a strong and varied program, showing the depth and breadth of current algorithms research. Three papers deserve special mentioning: the papers "When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings" by N. Bansal, A. Gupta, J. Li, J. Mestre, V. Nagarajan and A. Rudra and "Feasibility Analysis of Sporadic Real-Time Multiprocessor Task Systems" by V. Bonifaci and A. Marchetti-Spaccamela, which won the award for the best paper, and the paper "Shortest Paths in Planar Graphs with Real Lengths in O(n log2 n/ log log n) Time" by S. Mozes and C. Wulff-Nilsen, which won the award for the best student paper. We congratulate the authors on this succes. ESA 2010 was sponsored by the European Association of Theoretical Computer Science, the International Society of Computational Geometry, the London Mathematical Society, Springer, and the University of Liverpool. Besides the sponsors, we also wish to thank the people from the EasyChair Conference System; using their wonderful system saved us an enormous amount of work during the whole process. Finally, we thank all authors who submitted their work to ESA 2010, all Program Committee members for their hard work, and all reviewers who helped the Program Committees in evaluating the submitted papers, and we hope the readers will find the papers in these proceedings instructive and enjoyable

Algorithms - ESA 2010 : 18th annual European symposium, Liverpool, UK, September 6-8, 2010 : proceedings, part II

This volume contains the 69 papers presented at the 16th Annual European Symposium on Algorithms (ESA 2010), held in Liverpool during September 6–8, 2010, including three papers by the distinguished invited speakers Artur Czumaj, Herbert Edelsbrunner, and Paolo Ferragina. ESA 2010 was organized as a part of ALGO 2010, which also included the 10th Workshop on Algorithms in Bioinformatics (WABI), the 8th Workshop on Approximation and Online Algorithms (WAOA), and the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS). The European Symposium on Algorithms covers research in the design, use, and analysis of efficient algorithms and data structures. As in previous years, the symposium had two tracks: the Design and Analysis Track and the Engineering and Applications Track, each with its own Program Committee. In total 245 papers adhering to the submission guidelines were submitted. Each paper was reviewed by three or four referees. Based on the reviews and the often extensive electronic discussions following them, the committees selected 66 papers in total: 56 (out of 206) to the Design and Analysis Track and 10 (out of 39) to the Engineering and Applications track.We believe that these papers together made up a strong and varied program, showing the depth and breadth of current algorithms research. Three papers deserve special mentioning: the papers "When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings" by N. Bansal, A. Gupta, J. Li, J. Mestre, V. Nagarajan and A. Rudra and "Feasibility Analysis of Sporadic Real-Time Multiprocessor Task Systems" by V. Bonifaci and A. Marchetti-Spaccamela, which won the award for the best paper, and the paper "Shortest Paths in Planar Graphs with Real Lengths in O(n log2 n/ log log n) Time" by S. Mozes and C. Wulff-Nilsen, which won the award for the best student paper. We congratulate the authors on this succes. ESA 2010 was sponsored by the European Association of Theoretical Computer Science, the International Society of Computational Geometry, the London Mathematical Society, Springer, and the University of Liverpool. Besides the sponsors, we also wish to thank the people from the EasyChair Conference System; using their wonderful system saved us an enormous amount of work during the whole process. Finally, we thank all authors who submitted their work to ESA 2010, all Program Committee members for their hard work, and all reviewers who helped the Program Committees in evaluating the submitted papers, and we hope the readers will find the papers in these proceedings instructive and enjoyable

Algorithms - ESA 2010 : 18th annual European symposium, Liverpool, UK, September 6-8, 2010 : proceedings, part II

This volume contains the 69 papers presented at the 16th Annual European Symposium on Algorithms (ESA 2010), held in Liverpool during September 6–8, 2010, including three papers by the distinguished invited speakers Artur Czumaj, Herbert Edelsbrunner, and Paolo Ferragina. ESA 2010 was organized as a part of ALGO 2010, which also included the 10th Workshop on Algorithms in Bioinformatics (WABI), the 8th Workshop on Approximation and Online Algorithms (WAOA), and the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS). The European Symposium on Algorithms covers research in the design, use, and analysis of efficient algorithms and data structures. As in previous years, the symposium had two tracks: the Design and Analysis Track and the Engineering and Applications Track, each with its own Program Committee. In total 245 papers adhering to the submission guidelines were submitted. Each paper was reviewed by three or four referees. Based on the reviews and the often extensive electronic discussions following them, the committees selected 66 papers in total: 56 (out of 206) to the Design and Analysis Track and 10 (out of 39) to the Engineering and Applications track.We believe that these papers together made up a strong and varied program, showing the depth and breadth of current algorithms research. Three papers deserve special mentioning: the papers "When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings" by N. Bansal, A. Gupta, J. Li, J. Mestre, V. Nagarajan and A. Rudra and "Feasibility Analysis of Sporadic Real-Time Multiprocessor Task Systems" by V. Bonifaci and A. Marchetti-Spaccamela, which won the award for the best paper, and the paper "Shortest Paths in Planar Graphs with Real Lengths in O(n log2 n/ log log n) Time" by S. Mozes and C. Wulff-Nilsen, which won the award for the best student paper. We congratulate the authors on this succes. ESA 2010 was sponsored by the European Association of Theoretical Computer Science, the International Society of Computational Geometry, the London Mathematical Society, Springer, and the University of Liverpool. Besides the sponsors, we also wish to thank the people from the EasyChair Conference System; using their wonderful system saved us an enormous amount of work during the whole process. Finally, we thank all authors who submitted their work to ESA 2010, all Program Committee members for their hard work, and all reviewers who helped the Program Committees in evaluating the submitted papers, and we hope the readers will find the papers in these proceedings instructive and enjoyable

Improved Explicit Data Structures in the Bit-Probe Model Using Error-Correcting Codes

We consider the bit-probe complexity of the set membership problem: represent an n-element subset S of an m-element universe as a succinct bit vector so that membership queries of the form "Is x ? S" can be answered using at most t probes into the bit vector. Let s(m,n,t) (resp. s_N(m,n,t)) denote the minimum number of bits of storage needed when the probes are adaptive (resp. non-adaptive). Lewenstein, Munro, Nicholson, and Raman (ESA 2014) obtain fully-explicit schemes that show that s(m,n,t) = ?((2^t-1)m^{1/(t - min{2?log n?, n-3/2})}) for n ? 2,t ? ?log n?+1 . In this work, we improve this bound when the probes are allowed to be superlinear in n, i.e., when t ? ?(nlog n), n ? 2, we design fully-explicit schemes that show that s(m,n,t) = ?((2^t-1)m^{1/(t-{n-1}/{2^{t/(2(n-1))}})}), asymptotically (in the exponent of m) close to the non-explicit upper bound on s(m,n,t) derived by Radhakrishan, Shah, and Shannigrahi (ESA 2010), for constant n. In the non-adaptive setting, it was shown by Garg and Radhakrishnan (STACS 2017) that for a large constant n?, for n ? n?, s_N(m,n,3) ? ?{mn}. We improve this result by showing that the same lower bound holds even for storing sets of size 2, i.e., s_N(m,2,3) ? ?(?m)

The Unreasonable Success of Local Search: Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian plane: TSP with random inputs, Steiner tree with random inputs, facility location (with worst case inputs), and bicriteria $k$-median (also with worst case inputs). The randomness assumption is necessary for TSP