Weixiong Zhang - Profile on Academia.edu (original) (raw)
Papers by Weixiong Zhang
Artificial Intelligence, 1994
P&m,,, X, = X) = 1 (RCnyi 1970).
Artificial Intelligence, 1996
P&m,,, X, = X) = 1 (RCnyi 1970).
Distributed Breakout Revisited
Distributed breakout algorithm (DBA) is an effi- cient method for solving distributed constraint ... more Distributed breakout algorithm (DBA) is an effi- cient method for solving distributed constraint sat- isfaction problems (CSP). Inspired by its potential of being an efficient, low-overhead agent coordi- nation method for problems in distributed sensor networks, we study DBA' s properties in this paper. We specifically show that on an acyclic graph of nodes, DBA can find a solution in
BMC Plant Biology, 2008
Background: Small RNA-guided gene silencing at the transcriptional and post-transcriptional level... more Background: Small RNA-guided gene silencing at the transcriptional and post-transcriptional levels has emerged as an important mode of gene regulation in plants and animals. Thus far, conventional sequencing of small RNA libraries from rice led to the identification of most of the conserved miRNAs. Deep sequencing of small RNA libraries is an effective approach to uncover rare and lineage-and/or species-specific microRNAs (miRNAs) in any organism.
PLOS Computational Biology, 2007
MicroRNAs are short, noncoding RNAs that play important roles in post-transcriptional gene regula... more MicroRNAs are short, noncoding RNAs that play important roles in post-transcriptional gene regulation. Although many functions of microRNAs in plants and animals have been revealed in recent years, the transcriptional mechanism of microRNA genes is not well-understood. To elucidate the transcriptional regulation of microRNA genes, we study and characterize, in a genome scale, the promoters of intergenic microRNA genes in Caenorhabditis elegans, Homo sapiens, Arabidopsis thaliana, and Oryza sativa. We show that most known microRNA genes in these four species have the same type of promoters as protein-coding genes have. To further characterize the promoters of microRNA genes, we developed a novel promoter prediction method, called common query voting (CoVote), which is more effective than available promoter prediction methods. Using this new method, we identify putative core promoters of most known microRNA genes in the four model species. Moreover, we characterize the promoters of microRNA genes in these four species. We discover many significant, characteristic sequence motifs in these core promoters, several of which match or resemble the known cis-acting elements for transcription initiation. Among these motifs, some are conserved across different species while some are specific to microRNA genes of individual species. Citation: Zhou X, Ruan J, Wang G, Zhang W (2007) Characterization and identification of MicroRNA core promoters in four model species. PLoS Comput Biol 3(3): e37.
Artificial Intelligence, 2005
Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiabilit... more Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binary-clause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases. maximize the total weight of the satisfied clauses. Max-SAT and weighted max-SAT have many real-world applications in domains such as scheduling, configuration problems, probabilistic reasoning, auction, and pattern recognition . For simplicity, in this paper, when we mention max-SAT, we refer to both weighted and unweighted max-SAT. Following the convention for SAT, we refer to the ratio of the number of clauses to the number of variables as the "constrainedness" of max-SAT.
The difficulties in developing large-scale, distributed sensor networks are discussed and our rec... more The difficulties in developing large-scale, distributed sensor networks are discussed and our recent experience in developing and analyzing distributed problem solving methods for applications in sensor networks is overviewed.
Many distributed problems can be captured as distributed constraint satisfaction problems (CSPs) ... more Many distributed problems can be captured as distributed constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). In this research, we study an existing distributed search method, called distributed stochastic algorithm (DSA), and its variations for solving distributed CSPs and COPs. We analyze the relationship between the degree of parallel executions of distributed processes and DSAs' performance, including solution quality and communication cost. Our experimental results show that DSAs' performance exhibits phase-transition patterns. When the degree of parallel executions increases beyond some critical level, DSAs' performance degrades abruptly and dramatically, changing from near optimal solutions to solutions even worse than random solutions. Our experimental results also show that DSAs are generally more effective and efficient than distributed breakout algorithm on many network structures, particularly on over-constrained structures, finding better solutions and having lower communication cost. ¡
Efficient Strategies for (Weighted) Maximum Satisfiability
It is well known that the Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability (SAT... more It is well known that the Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability (SAT) can be extended to an algorithm for maximum SAT (max-SAT). In this paper, we propose a number of strategies to significantly improve this max-SAT method. The first strategy is a set of unit propagation rules; the second is an effective lookahead heuristic based on linear programming; and the third strategy is a dynamic variable ordering that exploits problem constrainedness during search. We integrate these strategies in an efficient complete solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from SATLIB demonstrate the efficacy of these strategies and show that the new solver is able to significantly outperform most of the existing complete max-SAT solvers, with a few orders of magnitude of improvement in running time in many cases.
This research is motivated by a distributed scheduling problem in distributed sensor networks, in... more This research is motivated by a distributed scheduling problem in distributed sensor networks, in which computational resources are scarce. To cope with limited computational resources and restricted real-time requirement, it is imperative to apply distributed algorithms that have low overhead on resource requirement and high anytime performance. In this paper, We study distributed stochastic algorithm (DSA) and distributed breakout algorithm (DBA), two distributed algorithms developed earlier for distributed constraint satisfaction problems. We experimentally investigate their properties and compare their performance using our distributed scheduling problem as a benchmark. We first formulate the scheduling problem as a distributed multi-coloring problem. We then experimentally show that the solution quality and communication cost of DSA exhibit phase-transition or threshold behavior, in that the performance degenerates abruptly and dramatically when the degree of parallel executions of distributed agents increases beyond some critical value. The results show that when controlled properly, DSA is superior to DBA, having better or competitive solution quality and significantly smaller communication cost than DBA. Therefore, DSA is the algorithm of choice for our distributed scan scheduling problem.
Distributed stochastic search and distributed breakout: properties, comparison and applications to constraint optimization problems in sensor networks
Artificial Intelligence, 2005
... We experimentally show that DSA has a phase-transition or threshold behavior, in that its sol... more ... We experimentally show that DSA has a phase-transition or threshold behavior, in that its solution quality degenerates abruptly and dramatically when the degree of parallel executions of distributed agents increases beyond some critical value. ...
In this and the following chapter, we consider what approaches one should take when one is confro... more In this and the following chapter, we consider what approaches one should take when one is confronted with a real-world application of the TSP. What algorithms should be used under which circumstances? We are in particular interested in the case where instances are too large for optimization to be feasible. Here theoretical results can be a useful initial guide, but the most valuable information will likely come from testing implementations of the heuristics on test beds of relevant instances. This chapter considers the symmetric TSP; the next considers the more general and less well-studied asymmetric case.
Depth-first branch-and-bound (DFBnB) is a complete algorithm that is typically used to find optim... more Depth-first branch-and-bound (DFBnB) is a complete algorithm that is typically used to find optimal solutions of difficult combinatorial optimization problems. It can also be adapted to an approximation algorithm and run as an anytime algorithm, which are the subjects of this paper. We compare DFBnB against the Kanellakis-Papadimitriou local search algorithm, the best known approximation algorithm, on the asymmetric Traveling Salesman Problem (ATSP), an important NP-hard problem. Our experimental results show that DFBnB significantly outperforms the local search on large ATSP and various ATSP structures, finding better solutions faster than the local search; and the quality of approximate solutions from a prematurely terminated DFBnB, called truncated DFBnB, is several times better than that from the local search.
The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests
The purpose of this paper is to provide a preliminary report on the first broad-based experimenta... more The purpose of this paper is to provide a preliminary report on the first broad-based experimental comparison of modern heuristics for the asymmetric traveling salesmen problem (ATSP). There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search algorithms based on re-arranging segments of the tour, as exemplified by the Kanellakis-Papadimitriou algorithm [KP80], and algorithms based on patching together the cycles in a minimum cycle cover, the best of which are variants on an algorithm proposed by Zhang [Zha93]. We test implementations of the main contenders from each class on a variety of instance types, introducing a variety of new random instance generators modeled on real-world applications of the ATSP. Among the many tentative conclusions we reach is that no single algorithm is dominant over all instance classes, although for each class the best tours are found either by Zhang’s algorithm or an iterated variant on Kanellakis-Papadimitriou.
We present a new algorithm that reduces the space complexity of heuristic search. It is most effe... more We present a new algorithm that reduces the space complexity of heuristic search. It is most effective for problem spaces that grow polynomially with problem size, but contain large numbers of short cycles. For example, the problem of finding an optimal global alignment of several DNA or amino-acid sequences can be solved by finding a lowest-cost corner-tocorner path in a -dimensional grid. A previous algorithm, called divide-and-conquer bidirectional search (Korf 1999), saves memory by storing only the Open lists and not the Closed lists. We show that this idea can be applied in a unidirectional search as well. This extends the technique to problems where bidirectional search is not applicable, and is more efficient in both time and space than the bidirectional version. If Ò is the length of the strings, and is the number of strings, this algorithm can reduce the memory requirement from Ç´Ò µ to Ç´Ò ½ µ. While our current implementation of DCFS is somewhat slower than existing dynamic programming approaches for optimal alignment of multiple gene sequences, DCFS is a more general algorithm.
Artificial Intelligence, 1995
that use space linear in the search depth are widely employed in practice to solve difficult prob... more that use space linear in the search depth are widely employed in practice to solve difficult problems optimally, such as planning and scheduling. In this paper, we study the average-case performance of linear-space search algorithms, including depth-first branch-andbound (DFBnB), iterative-deepening (ID), and recursive best-first search (RBFS). To facilitate our analyses, we use a random tree T( b, d) that has mean branching factor b, depth d, and node costs that are the sum of the costs of the edges from the root to the nodes. We prove that the expected number of nodes expanded by DFBnB on a random tree is no more than bd times the expected number of nodes expanded by best-first search (BFS) on the same tree, which usually requires space that is exponential in depth d. We also show that DFBnB is asymptotically optimal when BFS runs in exponential time, and ID and RBFS are asymptotically optimal when the edge costs of T( b,d) are integers. If bpo is the expected number of children of a node whose costs are the same as that of their parent, then the expected number of nodes expanded by these three linear-space algorithms is exponential when bpo < 1, at most 0( d4) when bpo = 1, and at most quadratic when bpo > 1. In addition, we study the heuristic branching factor of T( b, d) and the effective branching factor of BFS, DFBnB, ID, and RBFS on T( b, d). Furthermore, we use our analytic results to explain a surprising anomaly in the performance of these algorithms, and to predict the existence of a complexity transition in the Asymmetric Traveling Salesman Problem.
Truncated Branch-and-Bound: A Case Study on the Asymmetric TSP
... acknowledge helpful discussions with Richard Karp, David Johnson, Donald Miller, Joseph Pekny... more ... acknowledge helpful discussions with Richard Karp, David Johnson, Donald Miller, Joseph Pekny and Bruno Repetto, comments from David John-son ... 3] Carpaneto, G., and P. Toth, \Some new branch-ing and bounding criteria for the asymmetric trav-eling salesman problem ...
Artificial Intelligence, 1996
The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems... more The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Branch-and-bound (BnB) is the best method for finding an optimal solution of the TSP. Previous research has shown that there exists a transition in the average computational complexity of BnB on random trees. We show experimentally that when the intercity distances of the asymmetric TSP are drawn uniformly from {0,1,2,. . . , r}, the complexity of BnB experiences an easy-hard transition as r increases. We also observe easy-hard-easy complexity transitions when asymmetric intercity distances are chosen from a log-normal distribution. This transition pattern is similar to one previously observed on the symmetric TSP. We then explain these different transition patterns by showing that the control parameter that determines the complexity is the number of distinct intercity distances.
Journal of The ACM, 2005
The critical resource that limits the application of best-first search is memory. We present a ne... more The critical resource that limits the application of best-first search is memory. We present a new class of best-first search algorithms that reduce the space complexity. The key idea is to store only the Open list of generated nodes, but not the Closed list of expanded nodes. The solution path can be recovered by a divide-and-conquer technique, either as a bidirectional or unidirectional search. For many problems, frontier search dramatically reduces the memory required by best-first search. We apply frontier search to breadth-first search of sliding-tile puzzles and the 4-peg Towers of Hanoi problem, Dijkstra's algorithm on a grid with random edge costs, and the A* algorithm on the Fifteen Puzzle, the four-peg Towers of Hanoi Problem, and optimal sequence alignment in computational biology.
An Average-Case Analysis of Branch-and-Bound with Applications: Summary of Results
Artificial Intelligence, 1994
P&m,,, X, = X) = 1 (RCnyi 1970).
Artificial Intelligence, 1996
P&m,,, X, = X) = 1 (RCnyi 1970).
Distributed Breakout Revisited
Distributed breakout algorithm (DBA) is an effi- cient method for solving distributed constraint ... more Distributed breakout algorithm (DBA) is an effi- cient method for solving distributed constraint sat- isfaction problems (CSP). Inspired by its potential of being an efficient, low-overhead agent coordi- nation method for problems in distributed sensor networks, we study DBA&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; s properties in this paper. We specifically show that on an acyclic graph of nodes, DBA can find a solution in
BMC Plant Biology, 2008
Background: Small RNA-guided gene silencing at the transcriptional and post-transcriptional level... more Background: Small RNA-guided gene silencing at the transcriptional and post-transcriptional levels has emerged as an important mode of gene regulation in plants and animals. Thus far, conventional sequencing of small RNA libraries from rice led to the identification of most of the conserved miRNAs. Deep sequencing of small RNA libraries is an effective approach to uncover rare and lineage-and/or species-specific microRNAs (miRNAs) in any organism.
PLOS Computational Biology, 2007
MicroRNAs are short, noncoding RNAs that play important roles in post-transcriptional gene regula... more MicroRNAs are short, noncoding RNAs that play important roles in post-transcriptional gene regulation. Although many functions of microRNAs in plants and animals have been revealed in recent years, the transcriptional mechanism of microRNA genes is not well-understood. To elucidate the transcriptional regulation of microRNA genes, we study and characterize, in a genome scale, the promoters of intergenic microRNA genes in Caenorhabditis elegans, Homo sapiens, Arabidopsis thaliana, and Oryza sativa. We show that most known microRNA genes in these four species have the same type of promoters as protein-coding genes have. To further characterize the promoters of microRNA genes, we developed a novel promoter prediction method, called common query voting (CoVote), which is more effective than available promoter prediction methods. Using this new method, we identify putative core promoters of most known microRNA genes in the four model species. Moreover, we characterize the promoters of microRNA genes in these four species. We discover many significant, characteristic sequence motifs in these core promoters, several of which match or resemble the known cis-acting elements for transcription initiation. Among these motifs, some are conserved across different species while some are specific to microRNA genes of individual species. Citation: Zhou X, Ruan J, Wang G, Zhang W (2007) Characterization and identification of MicroRNA core promoters in four model species. PLoS Comput Biol 3(3): e37.
Artificial Intelligence, 2005
Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiabilit... more Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binary-clause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases. maximize the total weight of the satisfied clauses. Max-SAT and weighted max-SAT have many real-world applications in domains such as scheduling, configuration problems, probabilistic reasoning, auction, and pattern recognition . For simplicity, in this paper, when we mention max-SAT, we refer to both weighted and unweighted max-SAT. Following the convention for SAT, we refer to the ratio of the number of clauses to the number of variables as the "constrainedness" of max-SAT.
The difficulties in developing large-scale, distributed sensor networks are discussed and our rec... more The difficulties in developing large-scale, distributed sensor networks are discussed and our recent experience in developing and analyzing distributed problem solving methods for applications in sensor networks is overviewed.
Many distributed problems can be captured as distributed constraint satisfaction problems (CSPs) ... more Many distributed problems can be captured as distributed constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). In this research, we study an existing distributed search method, called distributed stochastic algorithm (DSA), and its variations for solving distributed CSPs and COPs. We analyze the relationship between the degree of parallel executions of distributed processes and DSAs' performance, including solution quality and communication cost. Our experimental results show that DSAs' performance exhibits phase-transition patterns. When the degree of parallel executions increases beyond some critical level, DSAs' performance degrades abruptly and dramatically, changing from near optimal solutions to solutions even worse than random solutions. Our experimental results also show that DSAs are generally more effective and efficient than distributed breakout algorithm on many network structures, particularly on over-constrained structures, finding better solutions and having lower communication cost. ¡
Efficient Strategies for (Weighted) Maximum Satisfiability
It is well known that the Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability (SAT... more It is well known that the Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability (SAT) can be extended to an algorithm for maximum SAT (max-SAT). In this paper, we propose a number of strategies to significantly improve this max-SAT method. The first strategy is a set of unit propagation rules; the second is an effective lookahead heuristic based on linear programming; and the third strategy is a dynamic variable ordering that exploits problem constrainedness during search. We integrate these strategies in an efficient complete solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from SATLIB demonstrate the efficacy of these strategies and show that the new solver is able to significantly outperform most of the existing complete max-SAT solvers, with a few orders of magnitude of improvement in running time in many cases.
This research is motivated by a distributed scheduling problem in distributed sensor networks, in... more This research is motivated by a distributed scheduling problem in distributed sensor networks, in which computational resources are scarce. To cope with limited computational resources and restricted real-time requirement, it is imperative to apply distributed algorithms that have low overhead on resource requirement and high anytime performance. In this paper, We study distributed stochastic algorithm (DSA) and distributed breakout algorithm (DBA), two distributed algorithms developed earlier for distributed constraint satisfaction problems. We experimentally investigate their properties and compare their performance using our distributed scheduling problem as a benchmark. We first formulate the scheduling problem as a distributed multi-coloring problem. We then experimentally show that the solution quality and communication cost of DSA exhibit phase-transition or threshold behavior, in that the performance degenerates abruptly and dramatically when the degree of parallel executions of distributed agents increases beyond some critical value. The results show that when controlled properly, DSA is superior to DBA, having better or competitive solution quality and significantly smaller communication cost than DBA. Therefore, DSA is the algorithm of choice for our distributed scan scheduling problem.
Distributed stochastic search and distributed breakout: properties, comparison and applications to constraint optimization problems in sensor networks
Artificial Intelligence, 2005
... We experimentally show that DSA has a phase-transition or threshold behavior, in that its sol... more ... We experimentally show that DSA has a phase-transition or threshold behavior, in that its solution quality degenerates abruptly and dramatically when the degree of parallel executions of distributed agents increases beyond some critical value. ...
In this and the following chapter, we consider what approaches one should take when one is confro... more In this and the following chapter, we consider what approaches one should take when one is confronted with a real-world application of the TSP. What algorithms should be used under which circumstances? We are in particular interested in the case where instances are too large for optimization to be feasible. Here theoretical results can be a useful initial guide, but the most valuable information will likely come from testing implementations of the heuristics on test beds of relevant instances. This chapter considers the symmetric TSP; the next considers the more general and less well-studied asymmetric case.
Depth-first branch-and-bound (DFBnB) is a complete algorithm that is typically used to find optim... more Depth-first branch-and-bound (DFBnB) is a complete algorithm that is typically used to find optimal solutions of difficult combinatorial optimization problems. It can also be adapted to an approximation algorithm and run as an anytime algorithm, which are the subjects of this paper. We compare DFBnB against the Kanellakis-Papadimitriou local search algorithm, the best known approximation algorithm, on the asymmetric Traveling Salesman Problem (ATSP), an important NP-hard problem. Our experimental results show that DFBnB significantly outperforms the local search on large ATSP and various ATSP structures, finding better solutions faster than the local search; and the quality of approximate solutions from a prematurely terminated DFBnB, called truncated DFBnB, is several times better than that from the local search.
The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests
The purpose of this paper is to provide a preliminary report on the first broad-based experimenta... more The purpose of this paper is to provide a preliminary report on the first broad-based experimental comparison of modern heuristics for the asymmetric traveling salesmen problem (ATSP). There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search algorithms based on re-arranging segments of the tour, as exemplified by the Kanellakis-Papadimitriou algorithm [KP80], and algorithms based on patching together the cycles in a minimum cycle cover, the best of which are variants on an algorithm proposed by Zhang [Zha93]. We test implementations of the main contenders from each class on a variety of instance types, introducing a variety of new random instance generators modeled on real-world applications of the ATSP. Among the many tentative conclusions we reach is that no single algorithm is dominant over all instance classes, although for each class the best tours are found either by Zhang’s algorithm or an iterated variant on Kanellakis-Papadimitriou.
We present a new algorithm that reduces the space complexity of heuristic search. It is most effe... more We present a new algorithm that reduces the space complexity of heuristic search. It is most effective for problem spaces that grow polynomially with problem size, but contain large numbers of short cycles. For example, the problem of finding an optimal global alignment of several DNA or amino-acid sequences can be solved by finding a lowest-cost corner-tocorner path in a -dimensional grid. A previous algorithm, called divide-and-conquer bidirectional search (Korf 1999), saves memory by storing only the Open lists and not the Closed lists. We show that this idea can be applied in a unidirectional search as well. This extends the technique to problems where bidirectional search is not applicable, and is more efficient in both time and space than the bidirectional version. If Ò is the length of the strings, and is the number of strings, this algorithm can reduce the memory requirement from Ç´Ò µ to Ç´Ò ½ µ. While our current implementation of DCFS is somewhat slower than existing dynamic programming approaches for optimal alignment of multiple gene sequences, DCFS is a more general algorithm.
Artificial Intelligence, 1995
that use space linear in the search depth are widely employed in practice to solve difficult prob... more that use space linear in the search depth are widely employed in practice to solve difficult problems optimally, such as planning and scheduling. In this paper, we study the average-case performance of linear-space search algorithms, including depth-first branch-andbound (DFBnB), iterative-deepening (ID), and recursive best-first search (RBFS). To facilitate our analyses, we use a random tree T( b, d) that has mean branching factor b, depth d, and node costs that are the sum of the costs of the edges from the root to the nodes. We prove that the expected number of nodes expanded by DFBnB on a random tree is no more than bd times the expected number of nodes expanded by best-first search (BFS) on the same tree, which usually requires space that is exponential in depth d. We also show that DFBnB is asymptotically optimal when BFS runs in exponential time, and ID and RBFS are asymptotically optimal when the edge costs of T( b,d) are integers. If bpo is the expected number of children of a node whose costs are the same as that of their parent, then the expected number of nodes expanded by these three linear-space algorithms is exponential when bpo < 1, at most 0( d4) when bpo = 1, and at most quadratic when bpo > 1. In addition, we study the heuristic branching factor of T( b, d) and the effective branching factor of BFS, DFBnB, ID, and RBFS on T( b, d). Furthermore, we use our analytic results to explain a surprising anomaly in the performance of these algorithms, and to predict the existence of a complexity transition in the Asymmetric Traveling Salesman Problem.
Truncated Branch-and-Bound: A Case Study on the Asymmetric TSP
... acknowledge helpful discussions with Richard Karp, David Johnson, Donald Miller, Joseph Pekny... more ... acknowledge helpful discussions with Richard Karp, David Johnson, Donald Miller, Joseph Pekny and Bruno Repetto, comments from David John-son ... 3] Carpaneto, G., and P. Toth, \Some new branch-ing and bounding criteria for the asymmetric trav-eling salesman problem ...
Artificial Intelligence, 1996
The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems... more The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Branch-and-bound (BnB) is the best method for finding an optimal solution of the TSP. Previous research has shown that there exists a transition in the average computational complexity of BnB on random trees. We show experimentally that when the intercity distances of the asymmetric TSP are drawn uniformly from {0,1,2,. . . , r}, the complexity of BnB experiences an easy-hard transition as r increases. We also observe easy-hard-easy complexity transitions when asymmetric intercity distances are chosen from a log-normal distribution. This transition pattern is similar to one previously observed on the symmetric TSP. We then explain these different transition patterns by showing that the control parameter that determines the complexity is the number of distinct intercity distances.
Journal of The ACM, 2005
The critical resource that limits the application of best-first search is memory. We present a ne... more The critical resource that limits the application of best-first search is memory. We present a new class of best-first search algorithms that reduce the space complexity. The key idea is to store only the Open list of generated nodes, but not the Closed list of expanded nodes. The solution path can be recovered by a divide-and-conquer technique, either as a bidirectional or unidirectional search. For many problems, frontier search dramatically reduces the memory required by best-first search. We apply frontier search to breadth-first search of sliding-tile puzzles and the 4-peg Towers of Hanoi problem, Dijkstra's algorithm on a grid with random edge costs, and the A* algorithm on the Fifteen Puzzle, the four-peg Towers of Hanoi Problem, and optimal sequence alignment in computational biology.
An Average-Case Analysis of Branch-and-Bound with Applications: Summary of Results