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There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
DSS serve the management, operations, and planning levels of an organization and help to make decisions, which may be rapidly changing and not easily specified in advance. Data mining has a vital role to extract important information to…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered…
Knowledge graphs have been shown to play a significant role in current knowledge mining fields, including life sciences, bioinformatics, computational social sciences, and social network analysis. The problem of link prediction bears many…
This paper quantifies the impact of branches and branch mispredictions on the single-core performance for two classes of graph problems. Specifically, we consider classical algorithms for computing connected components and breadth-first…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
Breadth First Search (BFS) is a building block for graph algorithms and has recently been used for large scale analysis of information in a variety of applications including social networks, graph databases and web searching. Due to its…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
The functional object-oriented network (FOON) has been developed as a knowledge representation method that can be used by robots in order to perform task planning. A FOON can be observed as a graph that can provide an ordered plan for…
A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. A partially complemented digraph $\widetilde{G}$ is a digraph obtained from a sequence of vertex complement…
Large Language Models have excelled in remarkable reasoning capabilities with advanced prompting techniques, but they fall short on tasks that require exploration, strategic foresight, and sequential decision-making. Recent works propose to…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
Rooted spanning trees (RSTs) are a core primitive in parallel graph analytics, underpinning algorithms such as biconnected components and planarity testing. On GPUs, RST construction has traditionally relied on breadth-first search (BFS)…
Computing bounded depth decompositions is a bottleneck in many applications of the treedepth parameter. The fastest known algorithm, which is due to Reidl, Rossmanith, S\'{a}nchez Villaamil, and Sikdar [ICALP 2014], runs in…
Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…