Questions tagged [dynamic-algorithms]

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What is the fastest deterministic algorithm for incremental DAG reachability?

As the title. The incremental algorithm maintains the reachability information of a DAG when it undergoes a series of edge insertions (but no deletions). And the algorithm supports constant query (if ...
13
votes
0answers
336 views

Applications of an access lemma for dynamic forests?

Sleator and Tarjan's amortized analysis of splay trees builds on their so-called Access Lemma. For purposes of analysis, assign an arbitrary weight to each node $v$, and let $size(v)$ denote the sum ...
3
votes
0answers
139 views

Dynamic matrix-matrix multiplication

Suppose A and B are initial Boolean matrices. Let C = A*B. Suppose one can perform the sequence of the next operations: "set A[i,j] = 1", "set B[i,j] = 1". The result of each ...
3
votes
0answers
106 views

Online bridge and nonbridge counting (identification)

I was wondering if there is any efficient (possibly armortized poly-logarithmic) online algorithm which supports counting (identification) of bridges- and non-bridges online, i.e. during a sequence of ...
2
votes
0answers
82 views

Dynamic connectivity with known history, for maximal connected component span

Consider a graph in which edges are added and removed over time. Define the span of a connected component as the product of its number of vertices and the longest duration for which it remains a ...
2
votes
0answers
51 views

2-dimensional dynamic set retrieval

For the following, $(w,x) >= (y,z)$ iff $w >= y$ and $x >= z$. I have a list, $L$, of $k$ points with integer coordinates ranging from $0$ to $n-1$. Each point has an associated set. I ...
1
vote
1answer
128 views

Dynamic transitive closure with immediate new reachability facts

The typical definition of dynamic transitive closure (or reachability) uses two types of queries: the first one is an update (edge deletion/insertion) and the second one is a reachability query. Thus, ...
1
vote
0answers
115 views

Algorithm for maximum bipartite matching with arriving edges?

Given a bipartite graph with fixed nodes and incrementally arriving edges, is there any efficient algorithm to compute and update the maximum matching?
1
vote
0answers
186 views

Relation between static Nash equlibria and dynamic equlibria

I am working on Normal form continuous games. I am not very familiar with dynamic game theory. I would like to know if there is any relation between static Nash equilibria and dynamic equilibria. If ...
1
vote
0answers
192 views

Dynamic k-shortest paths in a weighted transducer

I'm looking for references relating to dynamically computing the k-shortest output paths through a stochastic, acyclic, weighted transducer that is being constructed on-the-fly. In this scenario ...
0
votes
0answers
803 views

dynamic algorithms for the subset-sum problem hold for vectors?

I have a vector (er, array) that is the sum of a number of other known vectors. I would like to reverse the process and find the specific known vectors that were summed to make the final vector. The ...