Linear-time Dynamic Programming Algorithm Research Articles

EdgeWise: Energy-efficient CNN Computation on Edge Devices under Stochastic Communication Delays

This article presents a framework to enable the energy-efficient execution of convolutional neural networks (CNNs) on edge devices. The framework consists of a pair of edge devices connected via a wireless network: a performance and energy-constrained deviceDas the first recipient of data and an energy-unconstrained deviceNas an accelerator forD. DeviceDdecides on-the-fly how to distribute the workload with the objective of minimizing its energy consumption while accounting for the inherent uncertainty in network delay and the overheads involved in data transfer. These challenges are tackled by adopting the data-driven modeling framework of Markov Decision Processes, whereby an optimal policy is consulted byDinO(1) time to make layer-by-layer assignment decisions. As a special case, a linear-time dynamic programming algorithm is also presented for finding optimal layer assignment at once, under the assumption that the network delay is constant throughout the execution of the application. The proposed framework is demonstrated on a platform comprised of a Raspberry PI 3 asDand an NVIDIA Jetson TX2 asN. An average improvement of 31% and 23% in energy consumption is achieved compared to the alternatives of executing the CNNs entirely onDandN. Two state-of-the-art methods were also implemented and compared with the proposed methods.

On total [formula omitted]-domination: Polyhedral and algorithmic results

Given a graph G=(V,E) and integer values fv, v∈V, a node subset D⊂V is a total f-dominating set if every node v∈V is adjacent to at least fv nodes of D. Given a weight system c(v), v∈V, the minimum weight total f-dominating set problem is to find a total f-dominating set of minimum total weight. In this article, we propose a polyhedral study of the associated polytope together with a complete and compact description of the polytope for totally unimodular graphs and cycles. We also propose a linear time dynamic programming algorithm for the case of trees.

Folding Polyominoes into (Poly)Cubes

We study the problem of folding a polyomino [Formula: see text] into a polycube [Formula: see text], allowing faces of [Formula: see text] to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of [Formula: see text] or can divide squares in half (diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of [Formula: see text]), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of [Formula: see text]. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem, characterizing which polyiamonds fold into a regular tetrahedron.

On Automatic Formation of Effective Therapy Groups in Social Networks

Group therapy is one of the major clinical interventions to help patients with mental disorders. However, finding an effective therapy group is very challenging, since there are three crucial criteria that should be carefully considered simultaneously: 1) avoidance of isolation and loneliness; 2) unfamiliarity of patients; and 3) size of the therapy group. Manual selection of therapy group members, which is the common approach for most psychiatrists and mental health professionals today, may incur human bias and is very time-consuming. Therefore, we propose a new research problem, namely, Unfamiliarity-Aware Therapy Group Selection with Noah’s Ark Principle (UTNA) for automatic selections of therapy group members from the social network while addressing the three crucial criteria mentioned above. In this paper, we first analyze the NP-hardness and inapproximability of the UTNA problem. Then, we consider a special case of UTNA on trees, namely, Tree-based UTNA , and propose a linear-time dynamic programming algorithm to find the optimal solution. We then design an efficient algorithm, Effective Therapy Group Discovery , to select suitable members efficiently and effectively for the general UTNA problem. We invite 10 psychiatrists and clinical psychologists to conduct an expert study for validating our problem formulation, where all experts agree that our problem formulation is helpful for them, and the groups selected by our proposed approach are better than or similar to their manual configurations. In addition, we also conduct extensive experiments on three real data sets. Experimental results show that our proposed algorithms outperform other baselines in both efficiency and solution quality.

A Note on the Minimum H-Subgraph Edge Deletion

In this note we consider the following problem: Given a graph [Formula: see text] and a subgraph [Formula: see text], what is the smallest subset [Formula: see text] of edges in [Formula: see text] that needs to be deleted from the graph to make it [Formula: see text]-free? Several algorithmic results are presented. First, using the general framework of Courcelle [9], we show that, for a fixed subgraph [Formula: see text], the problem can be solved in linear time on graphs of bounded treewidth. It is known that the constant hidden in the big-O notation of Courcelle algorithm is big which makes the approach impractical. Thus, we present two explicit linear time dynamic programming algorithms on graphs of bounded treewidth for restricted settings of the problem with reasonable constants. Third, using the linear time algorithm for graphs of bounded treewidth, we design a Baker's type polynomial time approximation scheme for the problem on planar graphs.

Synthesis of first-order dynamic programming algorithms

To solve a problem with a dynamic programming algorithm, one must reformulate the problem such that its solution can be formed from solutions to overlapping subproblems. Because overlapping subproblems may not be apparent in the specification, it is desirable to obtain the algorithm directly from the specification. We describe a semi-automatic synthesizer of linear-time dynamic programming algorithms. The programmer supplies a declarative specification of the problem and the operators that might appear in the solution. The synthesizer obtains the algorithm by searching a space of candidate algorithms; internally, the search is implemented with constraint solving. The space of candidate algorithms is defined with a program template reusable across all linear-time dynamic programming algorithms, which we characterize as first-order recurrences. This paper focuses on how to write the template so that the constraint solving process scales to real-world linear-time dynamic programming algorithms. We show how to reduce the space with (i)~symmetry reduction and (ii)~domain knowledge of dynamic programming algorithms. We have synthesized algorithms for variants of maximal substring matching, an assembly-line optimization, and the extended Euclid algorithm. We have also synthesized a problem outside the class of first-order recurrences, by composing three instances of the algorithm template.

Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs

Consider the following restricted (symmetric or asymmetric) traveling-salesman problem (TSP): given an initial ordering of then cities and an integerk > 0, find a minimum-cost feasible tour, where ...