Algorithms for finding an element in some specified data-structure (most commonly, in a tree).

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65 views

What are the conditions that make the A* algorithm optimal over the other unidirectional search algorithms

I was wondering as what are the specific conditions which make the A* algorithm - optimal in terms of the node expansion over the other Unidirectional algorithms: When the same heuristic ...
3
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1answer
219 views

Is there a more efficient algorithm than backtracking/dynamic programming?

Consider the following game: One day a castle is attacked at sunrise (by surprise) by n soldiers. Each soldier carries a canon and a rifle. The castle has strength s. On the first day each ...
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1answer
23 views

Heuristic function

Is there any way to prove that an admissible heuristic may not be consistent? Most proof I came across are through examples .Is there a generalized proof?
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1answer
48 views

Karloff's algorithm applied to sparse graphs

I'm given a graph $G = (V, E)$ with $|V| = N$ and $|E| = m \ge N^{1+c}$ edges for some constant $c >0$. $G$ is called a $c$-dense graph. Karloff [1, p.6] has given a map-reduce algorithm called ...
2
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2answers
56 views

Finding a segment which has equal number of segments before and after it

I got this question in a past test that I'm trying to solve but i don't have the solutions to check my self: Given a set of n segments $[a_i ,b_i]$ where $i=1,..,n$ and $a_i < b_i$. write an ...
6
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1answer
392 views

Given an array of size N, if you know that all of the elements are white except for one, how to find the index of that element efficiently?

Yesterday while returning home, I walked past a house that had a camera. For some reason I started thinking about how these cameras work, and how you would use them in case of robbery. While thinking ...
2
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0answers
53 views

KMP Algorithm, Pratt's Minimisation/optimization of Knuth's original DFA based algorithm

The Original Knuth's Algorithm is based on DFA and it depends on the alphabet size. And Then, Pratt optimised it to be independent of Alphabet Size. But, All the ...
13
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4answers
483 views

Finding a pair of non-overlapping bit vectors

I give you a list of $n$ bitvectors of width $k$. Your goal is to return two bitvectors from the list that have no 1s in common, or else to report that no such pair exists. For example, if I give you ...
4
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1answer
113 views

Why aren't tries generally used?

To store say integers (positive), we prefer to use red black BSTs. I have never seen a explicit use of a trie anywhere to store numbers. I believe we can convert numbers to string and store them in ...
2
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3answers
99 views

Algorithm for finding all the combinations on a boolean array

I have to design an algorithm to do the next task: I have one array of booleans. For example: Array: [0 1 0 0 1 0 1 1] I want to obtain all the existing combinations of 1's, having in mind that ...
1
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1answer
30 views

Select the n closest nodes from a starting node in a weighted directed graph

I need to select a given number of nodes from a weighted directed graph such that the nodes selected are the closest to a given starting node. This seems like a common problem to need to solve, but I ...
0
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1answer
55 views

Binary tree node value maximization

Given a binary tree, construct the set of nodes whose sum is maximum subject to the restriction: if a node is included, its parent and children must be excluded, but grandchildren, etc. may be ...
0
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1answer
29 views

Order a list of edges to make the the complexity of searching for an edge O(lg E)

I was reading this article on how to represent graphs, and probably the simplest way to think about it is to have a list of edges, with an edget being usually a list of the vertices that are related ...
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0answers
44 views

Why is exact nearest neighbor search hard in high dimensional spaces?

I started research on nearest neighbor search in IR a couple of weeks ago. I am still very new to this field, but what I discovered so far from literature is: 1) For the exact nearest neighbor ...
2
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0answers
20 views

Why can't fractional cascading be used on two unrelated arrays?

According to both Wikipedia and my professor (see question 5.1), fractional cascading has to be done on arrays with related data. The specific question: A fellow student wants to compactly store ...
5
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1answer
44 views

Hamiltonian circuit for a family of graphs

For $\Sigma = \{a,b\}$, let $S_n = \{w\mid w \in \Sigma^{*} \land |w| = n\}$. Let $C_n \subset \Sigma^{*}$ be the language of circular strings that contain as substrings all elements of $S_n$. For ...
3
votes
1answer
136 views

Algorithm to search substring in a circular string?

I need an algorithm to search for substrings. I checked different resources, and it seems that the most known algorithms are the Boyer–Moore and the Knuth–Morris–Pratt. However, as far as I ...
3
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1answer
40 views

Minimum Length Hamiltonian Path Pair in O(n^2) or better

A friend and I have been discussing turning a $O(n^2)$ graph problem's algorithm into $O(n\log n)$, or at least less than $O(n^2)$. And no - this is not a homework question. We've narrowed it down to ...
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0answers
73 views

How to apply Alpha-Beta pruning to a game tree? (Algorithms Theory)

I'm studying for an AI exam, and having trouble working out this question on Alpha Beta pruning. I can answer on the effectiveness of the pruning method and the rules involved in the pruning process, ...
2
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1answer
47 views

Searching for multiple partial phrases so that one original phrase can not match multiple search phrases

Given a predefined set of phrases, I'd like to perform a search based on user's query. For example, consider the following set of phrases: ...
1
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1answer
29 views

An n-dimensional index where the search key specifies an exact match on certain dimensions?

I'm working on a project where I want to to search for vectors in the form (x1, x2, x3,...xn), and be able to search for them by specifying a specific x value and getting all vectors with that x value ...
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0answers
14 views

Effect of mismatches on string matching finite automata

I am contemplating a string matching FA algorithm (not KMP). The complexity of its transition function calculation ie the preprocessing is m(length of pattern )* (the language of the FA) . What effect ...
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0answers
66 views

graph algorithm to obtain all smallest largest paths [closed]

I would like to find all the best paths for the problem in this question The frog's longest Smallest Jump using a graph algorithm (note that for every set of stones there might be more than one ...
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0answers
87 views

How can I learn Sunday's string searching algorithm?

How does Sunday's string searching algorithm work? I am highly unskilled in processing mathematical lingo, so I would appreciate a use case/example. A link would be ok. I tried searching the first 6 ...
9
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2answers
635 views

What is a lay explanation for universal search?

I am reading a book on a computer science topic but lack some of the prerequisite background. Normally when I run into terms I don't understand I simply look them up, but for Universal Search I simply ...
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0answers
105 views

Iterative lengthening search: iterative version of Uniform Cost Search or DFS?

Actually my question has two parts: 1) I wanted to know that whether Iterative Lengthening Search is used in combination with DFS or Uniform Cost Search? Actually, in Russell and Norvig book (on page ...
4
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1answer
112 views

Finding all circuits that contain a given edge

Given a directed graph $G = (V, E)$ and an edge $e \in E$, I'm trying to come up with an algorithm to construct the minimum induced subgraph $H$ of $G$ with the property that every circuit in $G$ that ...
0
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1answer
70 views

Algorithm to determine two binary expression trees will give the same result based on associative and commutative properties of some operators

Given n different numbers, I would like to find out whether there exists an algebraic expression using all the n numbers, with n−1 binary operators and unlimited number of parentheses, that ...
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76 views

What data structure would help find nearby coordinates quickly?

I need to write a program that does the following: Take an input list of objects whose properties include latitude and longitude to, say, 5 decimal places Store them in a data structure once Provide ...
5
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1answer
265 views

What is the name for this search algorithm?

A colleague came up with the following search algorithm: We have an array of sorted, distinct integers [$i_0$ < $i_2$ < ... < $i_n$] We are looking for the index of $i_k$ (for simplicity ...
3
votes
2answers
71 views

Finding the lightest simple path in trees with integer weights

A tree with integer weights (positive, negative or zero) is given. We want to design an efficient algorithm for finding a simple path with lightest weight in this tree. That is, we look for shortest ...
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2answers
161 views

How to find the Branch factor of 8 Puzzle

I would like to know how to find the average branching factor for 8 puzzle.While referring Artificial Intelligence by George F Luger it says that: Suppose,for example we wish to establish the ...
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1answer
24 views

Is it possible to make excluded search with for loop in Java? [closed]

I am trying to calculate all pure strategy Nash equilibrium in a mxn game. It requires to check all pure strategy pairs (m.n pairs). Suppose player 1 has m strategies. Algorithm should start with the ...
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0answers
37 views

Given an algorithm, what are the probabilities for its run-time cases?

I am given this algorithm And I am also given the fact that $1 \leq k \leq n$. If we let X be the number of times line 2 is executed, then I am supposed to find the run-time probabilities for the ...
2
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0answers
38 views

Heuristic for weighted maximum independent set in graph with ~$2 \times 10^5$ nodes and $|E| \propto |V|$

I want to find a near-optimal solution for a maximum weight independent set. i.e given a graph $G = (V,E)$ I want to find a set $S = \{v_1,v_2,\dots,v_n\}$ of nodes in $V$ such that the sum of their ...
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0answers
4 views

Detecting junctions algorithmically

With route finding algorithms, we get the children of each node. So for example, an A* search on google maps at each point in the search would know which roads can be the successor to the current ...
0
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1answer
78 views

Heuristic for sokoban puzzle problem

I am trying to write IDA* for Sokoban puzzle problem (http://en.wikipedia.org/wiki/Sokoban) but It seems that my heuristic is not so good for making the algorithm fast. My heuristic is to consider ...
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3answers
45 views

Complexity of BST [duplicate]

I have the following pseudo-code for printing all nodes of a BST : ...
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3answers
121 views

Fastest possible way to check what of X is in a string

I am trying to speed up one of my application, one of the places where I can speed up is in my test if a string contains an array of strings. example: I have the matches "dog", "cat" "apple" and the ...
0
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1answer
86 views

Efficiently count frequency of n-grams at start of words

I have a text file with all possible 5-grams (26^5 = 11.881.376) organized in rows as: aaaaa aaaab aaaac aaaad ..... and I have a txt file (organized in rows) with all English words. I have to find ...
0
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0answers
36 views

Finding and Grouping like children

I'm working on a dependency managemen solution for a JavaScript. I'm trying to find the best pattern for grouping similar items in a graph into their own 'modules'. Given a dependency tree like ...
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0answers
47 views

Formulating an arrangement problem with STRIPS

The problem is rearranging furniture in a flat. We are given rectangular rooms of natural width and height with doors between them, (the walls have no width) and rectangular furniture at starting ...
1
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1answer
96 views

How to do high performance string matching when comparing unordered sets of tokens [closed]

This is the problem: I have some strings stored in the database. Each of the strings can be seen as a set of tokens separated by comma with no repetition (I mean a token cannot appear more than one ...
0
votes
1answer
74 views

Given two heuristic values how do I tell which one is admissible?

I am given 2 list of admissible values for a graph, and the graph with the real cost to each of the nodes. Am I correct in thinking the way to see which one is admissible is add up all the values of ...
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vote
2answers
418 views

Greedy and backtracking solutions to an arrangement problem with constraints

I'm revising for my finals. I have found a pattern in past papers in terms of a recurring question, reworded coming up every year. But I've no idea what the marker actually wants... I've asked class ...
3
votes
1answer
103 views

Efficient algorithm to find vertex with paths to every other vertex

$G=<V,E>$ is a directed graph. I need to write an efficient algorithm that finds a $v \in V$ such that there exists a path $\forall w \in V$ $v \rightarrow w$ ($v$ has a path to every other ...
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2answers
72 views

Why is it the lower the h(n) cost the more nodes need to be expanded in A*?

Why is it the lower the h(n) cost the more nodes need to be expanded in A*? As found here - http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html If h(n) is always lower than (or ...
0
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0answers
84 views

What is an algorithm that maps back and forth from (x,y) coordinates to the index of that point in a space filling curve over a rectangle?

Suppose that I have a space filling curve over a rectangle of width W and height H. For example, for the rectangle: ...
1
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1answer
72 views

negative effective branching factor it's possible?

i've implemented A* algorithm in python,after that i calculate with this python function the effective branching factor $ B^* $ $ T+1=1+B^*+(B^*)^2+⋯+(B^*)^L$ where $T$ is the number of expanded ...
0
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1answer
48 views

Why do heuristic functions only approximate the real value of the cost?

As stated in the title I'm wondering why do heuristic functions only approximate the real value of the cost? I understand it can never overestimate, but can it ensure the cost is accurate?