We consider the trade-offs in the choice between depth (a narrow high quality position) and breadth (a wide low quality range). In particular, the extent of depth or breadth in a market can be non-monotonic in the strength of competition.

Recent work shows that the memory requirements of bestfirst heuristic search can be reduced substantially by using a divide-and-conquer method of solution reconstruction. We show that memory requirements can be reduced even further by using a breadth-first instead of a best-first search strategy. We describe optimal and approximate breadth-first heuristic search algorithms that use divide-and-c...

A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...

In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic Breadth-First Search (LBFS) and prove its correctness. They believe that their corresponding 5-sweep LBFS interval graph recognition algorithm is also correct. Thanks to the LBFS structure theory established mainly by Corneil et al., we are able to present a 4-sweep...

Recently lexicographic breadth first search (LexBFS) has been shown to be a very powerful tool for the development of linear time, easily implementable recognition algorithms for various families of graphs. In this paper, we add to this work by producing a simple two LexBFS sweep algorithm to recognize the family of cographs. This algorithm extends to other related graph families such as P4-red...