# Questions tagged [ds.algorithms]

Questions regarding well-defined instructions for completing a task, and relevant analysis in terms of time/memory/etc.

394 questions with no upvoted or accepted answers
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249 views

### Atomic snapshot algorithms on tree-structured shared registers

Background: Atomic snapshot memory is a shared memory partitioned into words written (updated) by individual processes, or instantaneously read (scanned) in its entirety. The Gang of Six algorithm ...
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### Constant time search for rod segment

(I tried to ask at SO but maybe this has more to do with the CS theory.) Suppose I have a rod which I cut to pieces. Given a point on the original rod, is there a way to find out which piece it ...
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### Proving greedy algorithm is optimal for a scheduling problem

First, the problem discription: For a sequence of $4n$ tasks, $a_1a_2\dots a_{4n}$, where $a_i\in\{0,1\}\forall i$, put them sequentially to the tail of one of the two initially empty queues of ...
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What are some interesting open or solved-but-hard questions around problems having linear-time solutions? Ala riffle shuffles. I'm especially curious about problems which people believe to be linear-...
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### Linear programming - How to allow cycles with weight at most s?

Consider a graph $G=(V,E)$ with nonnegative weight function on the edges $w$. How would you express in LP that you want to allow cycles in $G$ with total weight at most $s$ ? I've found this while ...
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### Maximizing a convex function where the objective function is separable but the search space is not

The problem statement is Given convex functions $f_i$ over $X$, find $$\arg\max_{x\in X} \sum_i f_i(x)$$ Does this kind of problem structure allow one to use specific strategies to solve the ...
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### Randomized rounding on a graph

Assume we are given an arbitrary undirected graph $G = (V, E)$ where $|V| = n$. We are also given real numbers $x_e \in [0, 1]$ for each $e \in E$. These numbers satisfy the following constraint: \...
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### Polyhedral embedding from graph degree sequence

Given: A degree sequence. Wanted: A graph and a polyhedral embedding of this graph (described by a rotation system or something equivalent). By polyhedral embedding I mean only the combinatorial ...
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### Load-balancing; Alternate methods of keeping track of nodes?

Reading various articles in the literature have given me only a few decent methods of keeping track of nodes before->after load-balancing them on a very large network. One popular method uses virtual-...
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### Partitioning the vertices of a complete graph with weights on both vertices and edges with constraints

Given the complete graph on n vertices. Each vertex and each edge has a positive weight associated with it. What is desired is to partition the vertices into parts so that the sum of the weights of ...
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### K-shortest path in large sparse graph

I am an engineer and looking for a reference to find k-shortest path's in a large sparse graph. In the search for it, I came acorss Yen's ranking loopless algorithm and an improved implementation of ...
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### minimizing makespan for related machines

Any reference is appreciated. There are $n$ jobs and $m$ machines, machines has speeds and jobs have processing times. It takes $p_j/s_i$ units of time for machine $i$ with speed $s_i$ to process job ...
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### Distinguishing two types of Monte-Carlo algorithms

Recall from Wikipedia that Monte Carlo algorithm is a randomized algorithm whose running time is deterministic, but whose output may be incorrect with a certain (typically small) probability. Consider ...
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### Taking Square Roots of Matrices over Z/nZ

Is it easy (computationally) to take square roots of matrices over Z/nZ, if you know the factorization of n? More specifically, suppose I generate a random matrix M, and square it. Can a ...
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### worst case external fragmentation in buddy memory systems

Unfortunately, I can't find any freely available text with an estimation of exact upper bound of (external) fragmentation overhead for (binary) buddy memory allocator. Estimation $M(1+ \log 2 m)$ (...
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### Gram matrix of Max-Cut relaxation

It seems that Goemans and Williamson give a unique representation for each graph of the semidefinite relaxation (elements $y_{ij}$ of Y). However, semidefinite programming may give the same maximum ...
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### Optimization Problem on a Directed Graph

I have the following graph optimization problem. In a directed graph $G$, each node $i$ is endowed with a real value $v_i$ (input) that encodes the minimum "activation threshold" of that node. For ...
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### Is there a fast algorithm for computing the Schmidt decomposition

I have a huge covariance matrix, 𝑀, with the dimension, e.g., $10^8 \times 10^8$. Luckily enough, the number of nonzero eigenpairs, $n$, is very small, i.e., $n<5$. From the computational ...
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### What is the competitive ratio of a $d$-way associative LRU cache?

In a caching problem, items arrive online, and the algorithm needs to decide which elements to keep in the cache. If the current item is not cached, we pay a penalty of $1$. It is well known that for ...
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### On the goal of learned clause database reduction in CDCL SAT solvers

Modern SAT solvers frequently reduce the size of their learned clause database in order to keep its size as manageable as possible. This has as effect not to slow down the speed of unit propagations. ...
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### Career advice needed: Switching from theoretical CS to pure math

I couldn't think of a better forum to ask this question. I am a first year cs graduate student. I couldn't really pursue theoretical cs during my undergrad, but as part of our PhD qualifiers, i had to ...
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### Has Khachiyan/Porkolob's convex integer optimization been implemented?

Khachiyan and Porkolab in 'Integer optimization on convex semialgebraic sets' gave an $O(ld^{ O(k^4)})$ algorithm to minimize a degree $d$ form with integer coefficients of binary length at most $l$ ...
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### What is the difference between PRAM and multi threading?

PRAM and multi-threading are somewhat part of the same model of the shared memory model, in which both can compute in parallel, and both can allow processors to communicate with each other since there ...
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### Finding the largest set of points of limited diameter (2)

Problem: Given a set of points $S = \{(x_1, y_1), (x_2, y_2),\cdots,(x_n, y_n)\}$ in $\mathbb{R}^2$ and a distance threshold $\tau$, find a subset of $S$ such that (1) the Euclidean distance between ...
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### Is berklemap-massey works on extention field

According to the articles that i read (also wikipedia ), they refer that the above algorithm works on finite field $GF(q)$. But I cannot find an evidence that it still works on extension field, i.e:...
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### Standard basis for recurrence relations

In polynomial algebra there is a powerful tool for treating system of polynomial equations. It is standard or Groebner Bases. It allows to verify if system is consistent, eliminate variables, reduce ...
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### Non-Linear Programming with \min operator in the constraint

Can the following non-linear program be solved in polynomial time? $c_{ij}$'s are constants and known. Each $c_{ij}$ is either -1 or 1. \begin{align} \text{maximize } &\sum_{i,j=1}^{m,n} c_{ij}...
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### Nearest Common Ancestor on DFS Tree (with Addition of Leaves in DFS Order) on Pointer Machines

What is the complexity status for the Nearest Common Ancestor Problem on Trees in which the leaves are attached to the tree in DFS order ? i.e. Suppose one is visiting a tree T in DFS, and at any ...
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### Inclusion of polytopes

Consider the following two system of linear (in)eqaulities: $S = Ax \leq b;\; Cx = e$ $T = Dx \leq d;\; Gx = g$ How can I check if $S\cap \neg T=\emptyset$ where $\neg T$ is the complement of the ...
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### Claw finding using quantum walk: superposition for Szegedy's framework

Within Claw Finding Algorithms Using Quantum Walk there is the subroutine $claw_{detect}$ described. As in above paper: Let $J_f(N, l)$ and $J_G(M, m)$ be Johnson graphs. Let $F$ and $G$ be vertices ...
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### Forming Sets from 3-SAT Clauses

I'm wondering if someone can provide a good algorithm for the following problem. If we take 3-SAT in conjunctive normal form, we can partition some or all of the variables (not the literals) into ...