Searching in trees, series-parallel and interval orders
SIAM Journal on Computing
Optimal node ranking of trees in linear time
Information Processing Letters
Optimal edge ranking of trees in linear time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On an Optimal Split Tree Problem
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Searching in random partially ordered sets
Theoretical Computer Science - Latin American theorotical informatics
On the hardness of the minimum height decision tree problem
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Generalization of Binary Search: Searching in Trees and Forest-Like Partial Orders
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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
Edge ranking and searching in partial orders
Discrete Applied Mathematics
An Approximation Algorithm for Binary Searching in Trees
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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
Sorting and selection in posets
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Minimum average cost testing for partially ordered components
IEEE Transactions on Information Theory
On the Huffman and alphabetic tree problem with general cost functions
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Binary identification problems for weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Searching in dynamic tree-like partial orders
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The binary identification problem for weighted trees
Theoretical Computer Science
| Hi-index | 0.00 |
The well known binary search method can be described as the process of identifying some marked node from a line graph T by successively querying edges. An edge query e asks in which of the two subpaths induced by T \ e the marked node lies. This procedure can be naturally generalized to the case where T = (V,E) is a tree instead of a line. The problem of determining a tree search strategy minimizing the number of queries in the worst case is solvable in linear time [Onak etal. FOCS'06, Mozes et al. SODA'08]. Here we study the average-case problem, where the objective function is the weighted average number of queries to find a node An involved analysis shows that the problem is NP-complete even for the class of trees with bounded diameter, or bounded degree. We also show that any optimal strategy (i.e., one that minimizes the expected number of queries) performs at most O(Δ(T)(log |V | +log w (T))) queries in the worst case, where w(T) is the sum of the node weights and Δ(T) is the maximum degree of T. This structural property is then combined with a non-trivial exponential time algorithm to provide an FPTAS for the bounded degree case.