The Stack Overflow podcast is back! Listen to an interview with our new CEO.

# Questions tagged [ds.algorithms]

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

235 questions
Filter by
Sorted by
Tagged with
8answers
6k views

### Best Upper Bounds on SAT

In another thread, Joe Fitzsimons asked about "the best current lower bounds on 3SAT." I'd like to go the other way: What's the best current upper bounds on 3SAT? In other words, what is the time ...
93answers
109k views

### Algorithms from the Book.

Paul Erdos talked about the "Book" where God keeps the most elegant proof of each mathematical theorem. This even inspired a book (which I believe is now in its 4th edition): Proofs from the Book. If ...
17answers
7k views

### Polynomial-time algorithms with huge exponent/constant

Do you know sensible algorithms that run in polynomial time in (Input length + Output length), but whose asymptotic running time in the same measure has a really huge exponent/constant (at least, ...
9answers
13k views

### Powerful Algorithms too complex to implement

What are some algorithms of legitimate utility that are simply too complex to implement? Let me be clear: I'm not looking for algorithms like the current asymptotic optimal matrix multiplication ...
10answers
3k views

### Provable statements about genetic algorithms

Genetic algorithms don't get much traction in the world of theory, but they are a reasonably well-used metaheuristic method (by metaheuristic I mean a technique that applies generically across many ...
9answers
11k views

### Data for testing graph algorithms

I am looking for a source of huge data sets to test some graph algorithm implemention. Please also provide some information about the type/distribution (e.g. directed/undirected, simple/not simple, ...
5answers
2k views

### Positive topological ordering

Suppose I have a directed acyclic graph with real-number weights on its vertices. I want to find a topological ordering of the DAG in which, for every prefix of the topological ordering, the sum of ...
1answer
2k views

### Sorting algorithm, such that each element is compared $O(\log n)$ times, and doesn't depend on a sorting network

Are there any known comparison sorting algorithms that do not reduce to sorting networks, such that each element is compared $O(\log n)$ times? As far as I know, the only way to sort with $O(\log n)$ ...
2answers
929 views

### A reading list on experimental algorithmics

As in, the area of the papers in the ACM Journal on Experimental Algorithmic JEA. Which were the foundational works? What are the main results? How are they characterized? Any interesting connections ...
1answer
1k views

### Deciding emptiness of intersection of regular languages in subquadratic time

Let $L_1,L_2$ be two regular languages given by NFAs $M_1,M_2$ as input. Assume we would like to check whether $L_1\cap L_2\neq \emptyset$. This can clearly be done by a quadratic algorithm which ...
1answer
2k views

### computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
1answer
1k views

### Algorithm for optimizing decision trees

Background A binary decision tree $T$ is a rooted tree where each internal node (and root) is labeled by an index $j \in \{1,..., n\}$ such that no path from root to leaf repeats an index, the leafs ...
1answer
1k views

### Complexity of computing shortest paths in the plane with polygonal obstacles

Suppose we are given several disjoint simple polygons in the plane, and two points $s$ and $t$ outside every polygon. The Euclidean shortest path problem is to compute the Euclidean shortest path ...
11answers
10k views

### How hard is unshuffling a string?

A shuffle of two strings is formed by interspersing the characters into a new string, keeping the characters of each string in order. For example, MISSISSIPPI is a ...
8answers
4k views

### Are there non-constructive algorithm existence proofs?

I remember I might have encountered references to problems that have been proven to be solvable with a particular complexity, but with no known algorithm to actually reach this complexity. I struggle ...
6answers
12k views

### Complexity of Finding the Eigendecomposition of a Matrix

My question is simple: What is the worst-case running time of the best known algorithm for computing an eigendecomposition of an $n \times n$ matrix? Does eigendecomposition reduce to matrix ...
4answers
8k views

### Is there a hash function for a collection (i.e., multi-set) of integers that has good theoretical guarantees?

I'm curious whether there is a way to store a hash of a multi-set of integers that has the following properties, ideally: It uses O(1) space It can be updated to reflect an insertion or deletion in O(...
4answers
1k views

### Maximal classes for which largest independent set can be found in polynomial time?

The ISGCI lists over 1100 classes of graphs. For many of these we know whether INDEPENDENT SET can be decided in polynomial time; these are sometimes called IS-easy classes. I would like to compile ...
5answers
3k views

### Binary search generalizations for posets?

Suppose I have a poset "S" and a monotonic predicate "P" on S. I want to find one or all maximal elements of S satisfying P. EDIT: I'm interested in minimizing the number of evaluations of P. What ...
2answers
5k views

### Han's $O(n \log\log n)$ time, linear space, integer sorting algorithm

Is anyone familiar with Yijie Han's $O(n \log\log n)$, linear space, integer sorting algorithm? This result appears in a fairly short paper (Deterministic sorting in $O(n \log\log n)$ time and linear ...
4answers
3k views

### Counting words accepted by a regular grammar

Given a regular language (NFA, DFA, grammar, or regex), how can the number of accepting words in a given language be counted? Both "with exactly n letters" and "with at most n letters" are of ...
12answers
5k views

### What are some real world applications for genetic algorithms?

What are some real world problems that have been solved using a genetic algorithm? What is the problem? What is the fitness test used to solve this problem?
2answers
881 views

### What classes of mathematical programs can be solved exactly or approximately, in polynomial time?

I am rather confused by the continuous optimization literature and TCS literature about which types of (continuous) mathematical programs (MPs) can be solved efficiently, and which cannot. The ...
2answers
1k views

### Faster pseudo-polynomial time algorithms for PARTITION

I want to partition N given numbers (may or may not be equal) into 2 subsets such that the 2 subsets have sum as close as possible and also the cardinality of the sets are equal (if n is even) or ...
1answer
3k views

### Monotone bijections between lists of intervals

I have the following problem: Input: two sets of intervals $S$ and $T$ (all endpoints are integers). Query: is there a monotone bijection $f:S \to T$? The bijection is monotone w.r.t. the set ...
10answers
2k views

### #SAT Solver download

Could anyone please point to one or more websites where is possible to download a working implementation of a #SAT solver? I'm interested in those returning the exact solution count, not an ...
1answer
515 views

### techniques or examples of analyzing a series of graphs

Let there be a sequence of graphs $G_1, G_2, G_3, ...$ constructed using some particular approach or algorithm. in this particular case $G_n$ is constructed by modifying $G_{n-1}$ in some "systematic" ...
3answers
1k views

### Subgraph containing all nodes and edges that are part of length-limited simple s-t paths in an undirected graph

Quite similar to my previously posted question. This time however, the graph is undirected. Given An undirected graph $G$ with no multiple-edges or loops, A source vertex $s$, A target vertex $t$, ...
0answers
537 views

### State of the art for SAT solvers [duplicate]

Possible Duplicate: Best Upper Bounds on SAT I'm working on the obstruction-set-free grid coloring problem; a specific instance of it is described in this previous question on coloring 17x17 ...
6answers
45k views

### How do the state-of-the-art pathfinding algorithms for changing graphs (D*, D*-Lite, LPA*, etc) differ?

A lot of pathfinding algorithms have been developed in recent years which can calculate the best path in response to graph changes much faster than A* - what are they, and how do they differ? Are ...
17answers
8k views

### Examples of the price of abstraction?

Theoretical computer science has provided some examples of "the price of abstraction." The two most prominent are for Gaussian elimination and sorting. Namely: It is known that Gaussian elimination ...
10answers
10k views

### One Stack, Two Queues

background Several years ago, when I was an undergraduate, we were given a homework on amortized analysis. I was unable to solve one of the problems. I had asked it in comp.theory, but no ...
5answers
2k views

### Theoretical explanations for practical success of SAT solvers?

What theoretical explanations are there for the practical success of SAT solvers, and can someone give a "wikipedia-style" overview and explanation tying them all together? By analogy, the smoothed ...
6answers
2k views

### Which model of computation is “the best”?

In 1937 Turing described a Turing machine. Since then many models of computation have been decribed in attempt to find a model which is like a real computer but still simple enough to design and ...
1answer
1k views

### Toy Examples for Plotkin-Shmoys-Tardos and Arora-Kale solvers

I would like to understand how the Arora-Kale SDP solver approximates the Goemans-Williamson relaxation in nearly linear time, how the Plotkin-Shmoys-Tardos solver approximates fractional "packing" ...
4answers
2k views

### Starting SAT solver papers

I want to make a first SAT solver. I know the SAT competition and the SAT conference, and there are just so many papers on this subject. I'm a starter, an overwhelmed starter. Where should I begin? ...
8answers
3k views

4answers
1k views

### Positive topological ordering, take 3

Suppose we have an n by n matrix. Is it possible to reorder its rows and columns such that we get an upper-triangular matrix? This question is motivated by this problem: Positive topological ordering ...
1answer
8k views

### Finding the shortest path in the presence of negative cycles

Given a directed cyclic graph where the weight of each edge may be negative the concept of a "shortest path" only makes sense if there are no negative cycles, and in that case you can apply the ...
3answers
1k views

### How to produce a random graph that does not have a Hamiltonian cycle?

Let class A denote all the graphs of size $n$ which have a Hamiltonian cycle. It is easy to produce a random graph from this class--take $n$ isolated nodes, add a random Hamiltonian cycle and then add ...
4answers
2k views

### Complexity of applying a permutation in-place

To my surprise, I was not able to find papers about this - probably searched the wrong keywords. So, we've got an array of anything, and a function $f$ on its indices; $f$ is a permutation. How do ...
2answers
2k views

### Why is there an enormous difference between SAT solvers?

SAT solvers are very important in algebraic attacks, for example walksat and minisat. However, when solving the benchmark problems available here there is an enormous performance difference between ...
5answers
844 views

### References for Modular Decomposition

What are good papers/books to better understand the power of Modular Decomposition and its properties? I'm particularly interested in algorithmic aspects of Modular Decomposition. I have heard that ...
2answers
3k views

### Minimum number of transpositions to sort a list

In trying to devise my own sorting algorithm, I'm looking for the optimal benchmark to which I can compare it. For an unsorted ordering of elements A and a sorted ordering B, what is an efficient way ...