Variants Of Greedy Algorithms Research Articles

Advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) knapsack and covering problems, in which the constraints are exploited by means of surrogate constraint strategies. In addition, we provide a new graduated-probe strategy for improving the selection of variables to be assigned values. Going beyond the greedy and advanced greedy frameworks, we describe ways to utilize these algorithms with multi-start and strategic oscillation metaheuristics. Finally, we identify how surrogate constraints can be utilized to produce inequalities that dominate those previously proposed and tested utilizing linear programming methods for solving multi-constraint knapsack problems, which are responsible for the current best methods for these problems. While we focus on 0–1 problems, our approaches can readily be adapted to handle variables with general upper bounds.

Polynomially Improved Efficiency for Fast Parallel Single-Source Lexicographic Depth-First Search, Breadth-First Search, and Topological-First Search

Although lexicographic (lex) variants of greedy algorithms are often P -complete, NC -algorithms are known for the following lex-search problems: lexicographic depth-first search (lex-dfs) for dags [12], [17], lexicographic breadth-first search (lex-bfs) for digraphs [12], [17], and lexicographic topological-first search (lex-tfs) for dags [12]. For the all-sources version of the problem for dense digraphs, the lex-dfs (lex-bfs, lex-tfs) in [12] is (within a log factor of) work-optimal with respect to the all-sources sequential solution that performs a dfs (bfs, tfs) from every vertex. By contrast, to solve the single-source lexicographic version on inputs of size n , all known NC -algorithms perform work that is at least an n factor away from the work performed by their sequential counterparts.