Energy-Efficient Algorithms

We initiate the systematic study of the energy complexity of algorithms (in addition to time and space complexity) based on Landauer's Principle in physics, which gives a lower bound on the amount of energy a system must dissipate if it destroys information. We propose energy-aware variations of three standard models of computation: circuit RAM, word RAM, and transdichotomous RAM. On top of these models, we build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space and time complexity, enabling simple expression of energy-efficient algorithms. We analyze several classic algorithms in our models and develop low-energy variations: comparison sort, insertion sort, counting sort, breadth-first search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL trees, binary heaps, and dynamic arrays. We explore the time/space/energy trade-off and develop several general techniques for analyzing algorithms and reducing their energy complexity. These results lay a theoretical foundation for a new field of semi-reversible computing and provide a new framework for the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201

A MODIFIED PARTICLE SWARM OPTIMIZATION ALGORITHM FOR GENERAL INVERSE ORDERED p-MEDIAN LOCATION PROBLEM ON NETWORKS

This paper is concerned with a general inverse ordered p-median location problem on network where the task is to change (increase or decrease) the edge lengths and vertex weights at minimum cost subject to given modification bounds such that a given set of p vertices becomes an optimal solution of the location problem, i.e., an ordered p-median under the new edge lengths and vertex weights. A modified particle swarm optimization algorithm is designed to solve the problem under the cost functions related to the sum-type Hamming, bottleneck-type Hamming distances and the recti-linear and Chebyshev norms. By computational experiments, the high efficiency of the proposed algorithm is illustrated

Search Tracker: Human-derived object tracking in-the-wild through large-scale search and retrieval

Humans use context and scene knowledge to easily localize moving objects in conditions of complex illumination changes, scene clutter and occlusions. In this paper, we present a method to leverage human knowledge in the form of annotated video libraries in a novel search and retrieval based setting to track objects in unseen video sequences. For every video sequence, a document that represents motion information is generated. Documents of the unseen video are queried against the library at multiple scales to find videos with similar motion characteristics. This provides us with coarse localization of objects in the unseen video. We further adapt these retrieved object locations to the new video using an efficient warping scheme. The proposed method is validated on in-the-wild video surveillance datasets where we outperform state-of-the-art appearance-based trackers. We also introduce a new challenging dataset with complex object appearance changes.Comment: Under review with the IEEE Transactions on Circuits and Systems for Video Technolog

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

A Duality Exact Sequence for Legendrian Contact Homology

We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact homology CH_* which maps to singular homology. In particular, the sequence implies a duality between the kernel of the map (CH_*\to H_*) and the cokernel of the map (H_* \to CH^*). Furthermore, this duality is compatible with Poincare duality in L in the following sense: the Poincare dual of a singular class which is the image of a in CH_* maps to a class \alpha in CH^* such that \alpha(a)=1. The exact sequence generalizes the duality for Legendrian knots in Euclidean 3-space [24] and leads to a refinement of the Arnold Conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [6].Comment: 57 pages, 10 figures. Improved exposition and expanded analytic detai

A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters

In the Hausdorff Voronoi diagram of a family of \emph{clusters of points} in the plane, the distance between a point $t$ and a cluster $P$ is measured as the maximum distance between $t$ and any point in $P$, and the diagram is defined in a nearest-neighbor sense for the input clusters. In this paper we consider %El."non-crossing" \emph{non-crossing} clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, $n$, on the convex hulls of all clusters. We present a randomized incremental construction, based on point location, that computes this diagram in expected $O(n\log^2{n})$ time and expected $O(n)$ space. Our techniques efficiently handle non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions. The diagram finds direct applications in VLSI computer-aided design.Comment: arXiv admin note: substantial text overlap with arXiv:1306.583