Algorithms2014, 7(1), 62-144; doi:10.3390/a7010062 (doi registration under processing) - published online 7 March 2014 Show/Hide Abstract
Abstract: Dynamic programming is a classical algorithmic paradigm, which often allows the evaluation of a search space of exponential size in polynomial time. Recursive problem decomposition, tabulation of intermediate results for re-use, and Bellman’s Principle of Optimality are its well-understood ingredients. However, algorithms often lack abstraction and are difficult to implement, tedious to debug, and delicate to modify. The present article proposes a generic framework for specifying dynamic programming problems. This framework can handle all kinds of sequential inputs, as well as tree-structured data. Biosequence analysis, document processing, molecular structure analysis, comparison of objects assembled in a hierarchic fashion, and generally, all domains come under consideration where strings and ordered, rooted trees serve as natural data representations. The new approach introduces inverse coupled rewrite systems. They describe the solutions of combinatorial optimization problems as the inverse image of a term rewrite relation that reduces problem solutions to problem inputs. This specification leads to concise yet translucent specifications of dynamic programming algorithms. Their actual implementation may be challenging, but eventually, as we hope, it can be produced automatically. The present article demonstrates the scope of this new approach by describing a diverse set of dynamic programming problems which arise in the domain of computational biology, with examples in biosequence and molecular structure analysis.
Algorithms2014, 7(1), 32-59; doi:10.3390/a7010032 - published online 14 February 2014 Show/Hide Abstract
Abstract: We build an abstract model, closely related to the stable marriage problem and motivated by Hungarian college admissions. We study different stability notions and show that an extension of the lattice property of stable marriages holds in these more general settings, even if the choice function on one side is not path independent. We lean on Tarski’s fixed point theorem and the substitutability property of choice functions. The main virtue of the work is that it exhibits practical, interesting examples, where non-path independent choice functions play a role, and proves various stability-related results.
Algorithms2014, 7(1), 15-31; doi:10.3390/a7010015 - published online 11 February 2014 Show/Hide Abstract
Abstract: Emergency transportation plays a vital role in the success of disaster rescue and relief operations, but its planning and scheduling often involve complex objectives and search spaces. In this paper, we conduct a survey of recent advances in bio-inspired meta-heuristics, including genetic algorithms (GA), particle swarm optimization (PSO), ant colony optimization (ACO), etc., for solving emergency transportation problems. We then propose a new hybrid biogeography-based optimization (BBO) algorithm, which outperforms some state-of-the-art heuristics on a typical transportation planning problem.
Algorithms2014, 7(1), 1-14; doi:10.3390/a7010001 - published online 22 January 2014 Show/Hide Abstract
Abstract: We describe a flow model related to ordinary network flows the same way as stable matchings are related to maximum matchings in bipartite graphs. We prove that there always exists a stable flow and generalize the lattice structure of stable marriages to stable flows. Our main tool is a straightforward reduction of the stable flow problem to stable allocations. For the sake of completeness, we prove the results we need on stable allocations as an application of Tarski’s fixed point theorem.
Algorithms2013, 6(4), 871-882; doi:10.3390/a6040871 - published online 17 December 2013 Show/Hide Abstract
Abstract: This paper designs and evaluates a variant of CoSaMP algorithm, for recovering the sparse signal s from the compressive measurement given a fixed low-rank subspace spanned by U. Instead of firstly recovering the full vector then separating the sparse part from the structured dense part, the proposed algorithm directly works on the compressive measurement to do the separation. We investigate the performance of the algorithm on both simulated data and video compressive sensing. The results show that for a fixed low-rank subspace and truly sparse signal the proposed algorithm could successfully recover the signal only from a few compressive sensing (CS) measurements, and it performs better than ordinary CoSaMP when the sparse signal is corrupted by additional Gaussian noise.