Multistep greedy algorithm identifies community structure in real-world and computer-generated networks

We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width l that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions.Comment: 17 pages, 2 figure

Pilot, Rollout and Monte Carlo Tree Search Methods for Job Shop Scheduling

Greedy heuristics may be attuned by looking ahead for each possible choice, in an approach called the rollout or Pilot method. These methods may be seen as meta-heuristics that can enhance (any) heuristic solution, by repetitively modifying a master solution: similarly to what is done in game tree search, better choices are identified using lookahead, based on solutions obtained by repeatedly using a greedy heuristic. This paper first illustrates how the Pilot method improves upon some simple well known dispatch heuristics for the job-shop scheduling problem. The Pilot method is then shown to be a special case of the more recent Monte Carlo Tree Search (MCTS) methods: Unlike the Pilot method, MCTS methods use random completion of partial solutions to identify promising branches of the tree. The Pilot method and a simple version of MCTS, using the $\varepsilon$-greedy exploration paradigms, are then compared within the same framework, consisting of 300 scheduling problems of varying sizes with fixed-budget of rollouts. Results demonstrate that MCTS reaches better or same results as the Pilot methods in this context.Comment: Learning and Intelligent OptimizatioN (LION'6) 7219 (2012

Search algorithms for regression test case prioritization

Regression testing is an expensive, but important, process. Unfortunately, there may be insufficient resources to allow for the re-execution of all test cases during regression testing. In this situation, test case prioritisation techniques aim to improve the effectiveness of regression testing, by ordering the test cases so that the most beneficial are executed first. Previous work on regression test case prioritisation has focused on Greedy Algorithms. However, it is known that these algorithms may produce sub-optimal results, because they may construct results that denote only local minima within the search space. By contrast, meta-heuristic and evolutionary search algorithms aim to avoid such problems. This paper presents results from an empirical study of the application of several greedy, meta-heuristic and evolutionary search algorithms to six programs, ranging from 374 to 11,148 lines of code for 3 choices of fitness metric. The paper addresses the problems of choice of fitness metric, characterisation of landscape modality and determination of the most suitable search technique to apply. The empirical results replicate previous results concerning Greedy Algorithms. They shed light on the nature of the regression testing search space, indicating that it is multi-modal. The results also show that Genetic Algorithms perform well, although Greedy approaches are surprisingly effective, given the multi-modal nature of the landscape

Preferential attachment with choice

We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices according to a preferential rule and connects to the vertex in the selection with the $s$th highest degree. For meek choice, where $s>1$, we show that both double exponential decay of the degree distribution and condensation-like behaviour are possible, and provide a criterion to distinguish between them. For greedy choice, where $s=1$, we confirm that the degree distribution asympotically follows a power law with logarithmic correction when $r=2$ and shows condensation-like behaviour when $r>2$.Comment: 17 pages, 1 figure. Accepted for publication in Random Structures and Algorithm

Unfolding Convex Polyhedra via Radially Monotone Cut Trees

A notion of "radially monotone" cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut is infinitesimally opened by the curvature at the vertices along the path. It is shown that a class of planar, triangulated convex domains always have a radially monotone spanning forest, a forest that can be found by an essentially greedy algorithm. This algorithm can be mimicked in 3D and applied to polyhedra inscribed in a sphere. Although the algorithm does not provably find a radially monotone cut tree, it in fact does find such a tree with high frequency, and after cutting unfolds without overlap. This performance of a greedy algorithm leads to the conjecture that spherical polyhedra always have a radially monotone cut tree and unfold without overlap.Comment: 41 pages, 39 figures. V2 updated to cite in an addendum work on "self-approaching curves.

Matroids And Greedy Algorithms. A Deeper Justification of Using Greedy Approach To Find A Maximal set of a Matroid

Greedy algorithms are used in solving a diverse set of problems in small computation time. However, for solving problems using greedy approach, it must be proved that the greedy strategy applies. The greedy approach relies on selection of optimal choice at a local level reducing the problem to a single sub problem, which actually leads to a globally optimal solution. Finding a maximal set from the independent set of a matroid M(S, I) also uses greedy approach and justification is also provided in standard literature (e.g. Introduction to Algorithms by Cormen et .al.). However, the justification does not clearly explain the equivalence of using greedy algorithm and contraction of M by the selected element. This paper thus attempts to give a lucid explanation of the fact that the greedy algorithm is equivalent to reducing the Matroid into its contraction by selected element. This approach also provides motivation for research on the selection of the test used in algorithm which might lead to smaller computation time of the algorithm

Linear Parsing Expression Grammars

PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the classic formal language theory, it is significant and still challenging to argue PEGs' expressiveness in the context of formal language theory.Since PEGs are relatively new, there are several unsolved problems.One of the problems is revealing a subclass of PEGs that is equivalent to DFAs. This allows application of some techniques from the theory of regular grammar to PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of PEGs. Although the conversion judgement of parsing expressions into DFAs is undecidable in general, the formalism of LPEGs allows for a syntactical judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin

Adaptive Greedy versus Non-adaptive Greedy for Influence Maximization

We consider the \emph{adaptive influence maximization problem}: given a network and a budget $k$, iteratively select $k$ seeds in the network to maximize the expected number of adopters. In the \emph{full-adoption feedback model}, after selecting each seed, the seed-picker observes all the resulting adoptions. In the \emph{myopic feedback model}, the seed-picker only observes whether each neighbor of the chosen seed adopts. Motivated by the extreme success of greedy-based algorithms/heuristics for influence maximization, we propose the concept of \emph{greedy adaptivity gap}, which compares the performance of the adaptive greedy algorithm to its non-adaptive counterpart. Our first result shows that, for submodular influence maximization, the adaptive greedy algorithm can perform up to a $(1-1/e)$-fraction worse than the non-adaptive greedy algorithm, and that this ratio is tight. More specifically, on one side we provide examples where the performance of the adaptive greedy algorithm is only a $(1-1/e)$ fraction of the performance of the non-adaptive greedy algorithm in four settings: for both feedback models and both the \emph{independent cascade model} and the \emph{linear threshold model}. On the other side, we prove that in any submodular cascade, the adaptive greedy algorithm always outputs a $(1-1/e)$-approximation to the expected number of adoptions in the optimal non-adaptive seed choice. Our second result shows that, for the general submodular cascade model with full-adoption feedback, the adaptive greedy algorithm can outperform the non-adaptive greedy algorithm by an unbounded factor. Finally, we propose a risk-free variant of the adaptive greedy algorithm that always performs no worse than the non-adaptive greedy algorithm.Comment: 26 pages, 0 figure, accepted at AAAI'20: Thirty-Fourth AAAI Conference on Artificial Intelligenc