Partial fillup and search time in LC tries

Andersson and Nilsson introduced in 1993 a level-compressed trie (in short: LC trie) in which a full subtree of a node is compressed to a single node of degree being the size of the subtree. Recent experimental results indicated a 'dramatic improvement' when full subtrees are replaced by partially filled subtrees. In this paper, we provide a theoretical justification of these experimental results showing, among others, a rather moderate improvement of the search time over the original LC tries. For such an analysis, we assume that n strings are generated independently by a binary memoryless source with p denoting the probability of emitting a 1. We first prove that the so called alpha-fillup level (i.e., the largest level in a trie with alpha fraction of nodes present at this level) is concentrated on two values with high probability. We give these values explicitly up to O(1), and observe that the value of alpha (strictly between 0 and 1) does not affect the leading term. This result directly yields the typical depth (search time) in the alpha-LC tries with p not equal to 1/2, which turns out to be C loglog n for an explicitly given constant C (depending on p but not on alpha). This should be compared with recently found typical depth in the original LC tries which is C' loglog n for a larger constant C'. The search time in alpha-LC tries is thus smaller but of the same order as in the original LC tries.Comment: 13 page

Early Round Upsets and Championship Blowouts

In equilibrium play of a two-round tournament we find that underdogs exert more effort in the opening round while favorites save more effort for the final. Ability differences between players are therefore compressed in the opening round so upsets are more likely, and amplified in the final so blowouts are more likely. Measures that reduce the need to strategically allocate effort across games make for a more exciting final but a less exciting opening round. Consistent with the model, introduction of a one-day rest period between regional semi-final and final matches in the NCAA men’s basketball tournament was found to increase the favorite’s victory margin in the semi-finals by about five points. Non-sports applications of the model include the allocation of resources across primaries and general elections by candidates and the allocation of resources across a career ladder by managers.contest; tournament; all-pay auction

Risk Criteria for Approving or Rejecting Field Tests of High-Performance Weapons

Because details are classified and participation by affected populations is limited, military test ranges impose difficult challenges on those responsible for their safety. Here, the authors catalog some of those challenges and suggest ways to address them

Profiles of PATRICIA Tries

Digital trees are data structures that represent sets of strings according to their shared prefix structure