Level number sequences for trees
Discrete Mathematics
Upper and lower bounds on constructing alphabetic binary trees
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Searching in random partially ordered sets
Theoretical Computer Science - Latin American theorotical informatics
Decision trees for entity identification: approximation algorithms and hardness results
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Finding an optimal tree searching strategy in linear time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Optimal Binary Decision Trees
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Alphabetic coding with exponential costs
Information Processing Letters
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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We study a wide generalization of two classical problems, the Huffman Tree and Alphabetic Tree Problem. We assume that the cost caused by the ith leaf is fi(di), where di is its depth in the tree under consideration, and fi : N0 → R0+ is an arbitrary function. All solution methods known for the classical cases fail to compute the optimum here. For the generalized Alphabetic Tree Problem, we give a dynamic programming algorithm solving it in time O(n4), using space O(n3). Furthermore, we show that the runtime can be reduced to O(n3) if the cost functions are nondecreasing and convex. The improved algorithm can also be used in the setting where the cost functions are nondecreasing and the objective function is the maximum leaf cost. We also prove that the Huffman Tree Problem in its full generality is inapproximable unless P=NP, no matter if the objective function is the sum of leaf costs or their maximum. For the latter problem, we show that the case where the cost functions are nondecreasing admits a polynomial time algorithm.