The proceedings contain 180 papers. The topics discussed include: dynamic algorithms for graph coloring;incremental DFS algorithms: a theoretical and experimental study;decremental transitive closure and shortest path...
ISBN:
(纸本)9781611975031
The proceedings contain 180 papers. The topics discussed include: dynamic algorithms for graph coloring;incremental DFS algorithms: a theoretical and experimental study;decremental transitive closure and shortest paths for planar digraphs and beyond;polycubes with small perimeter defect;the classical complexity of boson sampling;race detection and reachability in nearly series-parallel DAGs;the complexity of independent set reconfiguration on bipartite graphs;metric violation distance: hardness and approximation;a submodular measure and approximate Gomory-Hu theorem for packing odd trails;and minor-matching hypertree width.
The proceedings contain 181 papers. The topics discussed include: a framework for similarity search with space-time tradeoffs using locality-sensitive filtering;LSH forest: practical algorithms made theoretical;faster...
ISBN:
(纸本)9781611974782
The proceedings contain 181 papers. The topics discussed include: a framework for similarity search with space-time tradeoffs using locality-sensitive filtering;LSH forest: practical algorithms made theoretical;faster approximation schemes for the two-dimensional knapsack problem;split packing: an algorithm for packing circles with optimal worst-case density;local search for max-sum diversification;maximum scatter tsp in doubling metrics;exploring an infinite space with finite memory scouts;parameter-free locality sensitive hashing for spherical range reporting;distance sensitive bloom filters without false negatives;optimal approximate polytope membership;and massively-parallel similarity join, edge-isoperimetry, and distance correlations on the hypercube.
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions ...
ISBN:
(纸本)9781510819672
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions in group testing;tight bounds for the distribution-free testing of monotone conjunctions;designing networks with good equilibria under uncertainty;characterization of strongly stable matchings;learning and efficiency in games with dynamic population;on dynamic approximate shortest paths for planar graphs with worst case costs;error amplification for pairwise spanner lower bounds;on notions of distortion and an almost minimum spanning tree with constant average distortion;approximately efficient double auctions with strong budget balance;and interpolating between truthful and non-truthful mechanisms for combinatorial auctions.
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions ...
ISBN:
(纸本)9781510819672
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions in group testing;tight bounds for the distribution-free testing of monotone conjunctions;designing networks with good equilibria under uncertainty;characterization of strongly stable matchings;learning and efficiency in games with dynamic population;on dynamic approximate shortest paths for planar graphs with worst case costs;error amplification for pairwise spanner lower bounds;on notions of distortion and an almost minimum spanning tree with constant average distortion;approximately efficient double auctions with strong budget balance;and interpolating between truthful and non-truthful mechanisms for combinatorial auctions.
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions ...
ISBN:
(纸本)9781510819672
The proceedings contain 146 papers. The topics discussed include: locality-sensitive hashing without false negatives;new directions in nearest neighbor searching with applications to lattice sieving;phase transitions in group testing;tight bounds for the distribution-free testing of monotone conjunctions;designing networks with good equilibria under uncertainty;characterization of strongly stable matchings;learning and efficiency in games with dynamic population;on dynamic approximate shortest paths for planar graphs with worst case costs;error amplification for pairwise spanner lower bounds;on notions of distortion and an almost minimum spanning tree with constant average distortion;approximately efficient double auctions with strong budget balance;and interpolating between truthful and non-truthful mechanisms for combinatorial auctions.
Generating orthonormal Laguerre- Gaussian-power-like eigenvectors of the symmetric kernel matrix T of the discrete Hankel transform ( DHT) is the cornerstone in developing the discrete fractional Hankel transform (DFR...
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ISBN:
(纸本)9798350387186;9798350387179
Generating orthonormal Laguerre- Gaussian-power-like eigenvectors of the symmetric kernel matrix T of the discrete Hankel transform ( DHT) is the cornerstone in developing the discrete fractional Hankel transform (DFRHT). The direct sequential generation of the columns of each partition of the modal matrix of matrix T pertaining to one distinct eigenvalue is considered. The focus of the research is the assessment of the direct sequential algorithms: the Gram-Schmidt algorithm (GSA), modified Gram-Schmidt algorithm (MGSA), sequential orthogonal procrustes algorithm (SOPA) and direct sequential evaluation by constrained optimization algorithm (DSEOA). Although the four algorithms are theoretically equivalent, they are quite numerically distinct. The difference in performance becomes more pronounced as the order of the square matrix T becomes larger. The assessment shows that the MGSA outperforms both the GSA and the SOPA and that the DSEOA is by far the best in terms of computation accuracy.
Given a d-dimensional continuous (resp. discrete) probability distribution mu and a discrete distribution nu, the semi-discrete (resp. discrete) optimal transport (OT) problem asks for computing a minimum-cost plan to...
ISBN:
(纸本)9781611977912
Given a d-dimensional continuous (resp. discrete) probability distribution mu and a discrete distribution nu, the semi-discrete (resp. discrete) optimal transport (OT) problem asks for computing a minimum-cost plan to transport mass from mu to nu;we assume n to be the number of points in the support of the discrete distributions. In this paper, we present three approximation algorithms for the OT problem with strong provable guarantees. (i) Additive approximation for semi-discrete OT: For any parameter epsilon > 0, we present an algorithm that computes a semi-discrete transport plan (tau) over tilde with cost cent((tau) over tilde) <= cent(tau*) + epsilon in n(O(d)) log D/epsilon time;here, tau* is the optimal transport plan, D is the diameter of the supports of mu and nu, and we assume we have access to an oracle that outputs the mass of mu inside a constant-complexity region in O(1) time. Our algorithm works for several ground distances including the L-p-norm and the squared-Euclidean distance. (ii) Relative approximation for semi-discrete OT: For any parameter epsilon > 0, we present an algorithm that computes a semi-discrete transport plan (tau) over tilde with cost cent((tau) over tilde) <= (1 + epsilon)cent(tau*) in n log(n) . (epsilon(-1) log log n)(O(d)) expected time;here, tau* is the optimal transport plan, and we assume we have access to an oracle that outputs the mass of mu inside an orthogonal box in O(1) time, and the ground distance is any L-p norm. (iii) Relative approximation for discrete OT: For any parameter epsilon > 0, we present a Monte-Carlo algorithm that computes a transport plan (tau) over tilde with an expected cost cent((tau) over tilde) <= (1 + epsilon)cent(tau*) under any L-p norm in n log(n) . (epsilon(-1) log log n)(O(d)) time;here, tau* is an optimal transport plan and we assume that the spread of the supports of mu and nu is polynomially bounded.
We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only ...
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ISBN:
(纸本)9798400703836
We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only loses an excess logarithmic factor in the aspect ratio of the polytope. Our algorithms are nearly optimal in two senses: first, their runtimes nearly match those of the most efficient known algorithms for the offline version of the problem. Second, their approximation factors nearly match a lower bound we show against a natural class of geometric streaming algorithms. In contrast to existing works in the streaming setting that compute ellipsoidal roundings only for centrally symmetric convex polytopes, our algorithms apply to general convex polytopes. We also show how to use our algorithms to construct coresets from a stream of points that approximately preserve both the ellipsoidal rounding and the convex hull of the original set of points.
The single-source unsplittable flow (SSUF) problem asks to send flow from a common source to different terminals with unrelated demands, each terminal being served through a single path. One of the most heavily studie...
ISBN:
(纸本)9781611977912
The single-source unsplittable flow (SSUF) problem asks to send flow from a common source to different terminals with unrelated demands, each terminal being served through a single path. One of the most heavily studied SSUF objectives is to minimize the violation of some given arc capacities. A seminal result of Dinitz, Garg, and Goemans showed that, whenever a fractional flow exists respecting the capacities, then there is an unsplittable one violating the capacities by at most the maximum demand. Goemans conjectured a very natural cost version of the same result, where the unsplittable flow is required to be no more expensive than the fractional one. This intriguing conjecture remains open. More so, there are arguably no non-trivial graph classes for which it is known to hold. We show that a slight weakening of it (with at most twice as large violations) holds for planar graphs. Our result is based on a connection to a highly structured discrepancy problem, whose repeated resolution allows us to successively reduce the number of paths used for each terminal, until we obtain an unsplittable flow. Moreover, our techniques also extend to simultaneous upper and lower bounds on the flow values. This also affirmatively answers a conjecture of Morell and Skutella for planar SSUF.
We consider the problem of building numerically stable algorithms for computing discrete Fourier Transform (DFT) of N- length signals with known frequency support of size k. A typical algorithm, in this case, would in...
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ISBN:
(纸本)9798350382853;9798350382846
We consider the problem of building numerically stable algorithms for computing discrete Fourier Transform (DFT) of N- length signals with known frequency support of size k. A typical algorithm, in this case, would involve solving (possibly poorly conditioned) a system of equations, causing numerical instability. When N is a power of 2, and the frequency support is a random subset of Z(N), we provide an algorithm that has (a possibly optimal) O(k log k) complexity to compute the DFT while solving system of equations that are O(1) in size.
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