Characterizations of Non-simple Greedoids and Antimatroids based on Greedy Algorithms
نویسنده
چکیده
A language containing no words with repeated elements is simple. And a language which is not necessary simple is called non-simple in this paper. Björner and Ziegler [3] presented three plausible extensions of greedoids to non-simple languages. We shall show that when choosing one of their definitions they called ’polygreedoid’ and replacing generalized bottleneck functions of the objective function by an extended notion defined in this note, the algorithmic characterization of (simple) greedoids by Goecke, Korte and Lovász [7] can be naturally generalized to non-simple greedoids. Björner, Lovász and Shor [2] introduced non-simple antimatroids relating to chip-firing games on graphs. We also show that the algorithmic characterization of (simple) antimatroids established by Boyd and Faigle [4] can be similarly extended to non-simple antimatroids as well.
منابع مشابه
Antimatroids, Betweenness, Convexity
Korte and Lovász [12, 13] founded the theory of greedoids . These combinatorial structures characterize a class of optimization problems that can be solved by greedy algorithms. In particular, greedoids generalize matroids , introduced earlier by Whitney [16]. Antimatroids , introduced by Dilworth [3] as particular examples of semimodular lattices, make up another class of greedoids. Antimatroi...
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