# Questions tagged [intervals]

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### Best algorithm to find "deepest" interval

Let's say I have a list of intervals on a number line. The "depth" of a point on this number line corresponds to the number of intervals in the list that contain it [the point]. So for ...
44 views

### Weighted maximum match for intervals

Say I have two sets of intervals sorted by time $I_1=[(x_1, y_1),... (x_n, y_n)]$ and $I_2 = [(a_1, b_1)... (a_m, b_m)]$. where $x, y, a, b$ are times in seconds. None of the intervals within $I_1$ ...
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### Social Networking Disease Transmission

You are given an undirected graph (social network) in which each edge $e = (v, v')$ has an interval $I_e = [l_e, u_e]$ on it. The meaning is that you know that $v$ and $v'$ met at some point during ...
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### Maximum interval scheduling - Circular Variation

Consider a variant of interval scheduling except now the intervals are arcs on a circle. The goal is to find the maximum number of arcs that do not overlap. Let $C$ be the circle on the plane centered ...
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### Efficient 2d interval merging product

Suppose I have two tables of 2d intervals (axis-aligned rectangles) with values attributed to each interval. ...
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### Finding a rainbow independent set in a circle

Inside the interval $[0,1]$, there are $n^2$ intervals of $n$ different colors: $n$ intervals of each color. The intervals of each color are pairwise-disjoint. A rainbow independent set is a set of $n$...
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### Finding max values at a point given a list of ranges

In coding competitions I usually see problems that involve dealing with values in given ranges. A typical example is, given a list of 3-tuples defined as so ...
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### Merging Tuples of Intervals

Suppose I have a list of tuples. Each tuple contains 2 intervals. The intervals in each tuple have nothing to do with each other. I would like to find a smaller list of tupels that covers all elements ...
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### Optimality of DSATUR on interval graphs

The DSATUR algorithm is a greedy graph coloring algorithm. It consists of applying the usual greedy coloring algorithm, considering vertices in reverse lexicographic order of (number of different ...
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### Minimal number of intervals that covers $\{1,...,k\}$

Let $F$ be a family of sets of consecutive integers in $\{1,…,k\}$ that is closed under taking subintervals, i.e. for any $a≤b≤c≤d$, if $\{a,…,d\} \in F$, then $\{b,…,c\} \in F$ also. Find a minimum ...
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### What's the name of this packing problem?

I'm trying to pack sets of intervals, to find distinct buckets of intervals. The buckets should not be overlapping. For example if I have these intervals: ...
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### Intersection of Decision Tree Boundaries in Higher Dimensions

I have trained two binary decision tree classifiers with splits in $\mathbb{R}^4$. Same data, but from two different patches. Now, I want to find the exact intervals where the two trees disagree. The ...
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### Data structure for interval subset queries

I have a set $S$ of intervals. I'd like to store them in a data structure, so that I can handle the following query efficiently: given a query interval $q$, count the number of intervals $s \in S$ ...
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### Find minimum number of points which intersect overlapping arcs

Say I have a circle of a fixed radius, with overlapping arc intervals along its edge. I want to return a minimum set of Points which intersects all arcs in $n^2$ time. I'm having some trouble proving ...
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### How can I implement a data structure which calculates the number of nested intervals in sub-linear time?

Is there a data structure which can maintain a list of intervals and the following operations? ...
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### What does it mean that a set of intervals is sorted by the right and left endpoints?

While reading a paper (On the k-coloring of intervals), I came upon the following description: "Input: An integer k, and a set of n intervals sorted by right and left endpoints. The intervals are ...
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### Algorithm To Compute The Gaps Between A Set of Intervals

Problem Given a set of intervals with possibly non-distinct start and end points, find all maximal gaps. A gap is defined as an interval that does not overlap with any given interval. All endpoints ...
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### Intervals Collision Detection Algorithm

Given a collection of non-empty intervals [a,b), where a/b are integers in some finite range (ex. 0...100) and a is less than b, can you find an algorithm that will detect all intervals that exhibit ...
202 views

### How to group intervals which overlap by some amount?

I have an algorithm that generates a list of intervals. The algorithm is run m times. Lets mark the intervals as tuples (s1, e1), (s2, e2), .., (sn, en). It is ...
108 views

### Is it posssible to calculate the intersection area of rectangles with sweep Line and Interval or Segment Tree

I am curently working on automatic label placement, so for evaluating a model, one metric is to calculate the Area A: A is the sum of every part of a rectangle covered by another. So if two rectangle ...
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### Returning random integer from interval based on last result and a seed

Suppose we have an interval of integers [a, b]. I would like to have a function that returns random members from within the interval, without repetitions. Once that all members within the interval are ...
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### Is there an Interval Tree which supports O(1) dynamic space requirements for queries?

I observed that all the interval tree implementations I am able to come up with are required to utilize a stack (or a-like) to answer queries (report any overlapping interval with a key). In general ...
48 views

### Why does a range query on a segment tree return at most $\lceil \log_2{N} \rceil$ nodes?

If an array $A[1 \ldots N]$ is represented using a segment tree having sets in each interval, why does a range query $[L\ldots R]$ returns at most $\lceil \log_2{N} \rceil$ sets (or disjoint intervals)...
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### Interval sorting that avoids covering

I have a collection of intervals and I want to sort them so that the order is interpreted as a sort of "z-index". That is, a given interval may or may not be "visible" depending on whether the merge ...
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### Schedule X Classes In N Classrooms

I would really appreciate any thought on this, or under which category does this problem fall (Interval scheduling, Interval partitioning,...) I am really out of thoughts I have X number of classes ...
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### Max clique in interval graph

According to Efficient algorithms for interval graphs and circular arc graphs there is an $O(n \log n)$ algorithm for finding the max clique in an interval graph, assuming you have the interval model. ...
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### How Segment trees are used to answer interval stabbing query?

Can anybody explain to me how segment trees are used to answer interval stabbing queries? I have searched and searched and only come with the beginning of the line. From my understanding I need to ...
192 views

### largest subset of pairwise intersecting intervals [closed]

Given a set of intervals on the real line, compute the largest subset of pairwise intersecting intervals (an interval in the subset must intersect with every other interval in the subset). Design a ...
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### Algorithm for detecting overlaps

This is a real-world application, not a student assignment. Suppose a list of events of that have startTime and endTime, and ...
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### interval scheduling algorithm

can any one explain why the greedy algorithm solution i.e sorting according to finishing time is optimal in the interval scheduling algorithm ?? I want proof in layman's language. I was watching this ...
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### Variant of interval scheduling with varying task durations

I am probably just missing the correct term for my problem to find the solution but here it goes: I have a set of tasks with a given duration and an interval for each task in which it has to be ...