| 1. |
- Berkholz, C., et al.
(författare)
-
Supercritical space-width trade-offs for resolution
- 2016
-
Ingår i: Leibniz International Proceedings in Informatics, LIPIcs. - : Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. - 9783959770132
-
Konferensbidrag (refereegranskat)abstract
- We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width resolution proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the space-width trade-offs in [Ben- Sasson 2009], and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [Razborov 2016]. We obtain our results by using Razborov's new hardness condensation technique and combining it with the space lower bounds in [Ben-Sasson and Nordström 2008].
|
|
| 3. |
- Chiesa, Marco, 1987-, et al.
(författare)
-
On the resiliency of randomized routing against multiple edge failures
- 2016
-
Ingår i: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016. - : Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. - 9783959770132
-
Konferensbidrag (refereegranskat)abstract
- We study the Static-Routing-Resiliency problem, motivated by routing on the Internet: Given a graph G = (V, E), a unique destination vertex d, and an integer constant c > 0, does there exist a static and destination-based routing scheme such that the correct delivery of packets from any source s to the destination d is guaranteed so long as (1) no more than c edges fail and (2) there exists a physical path from s to d? We embark upon a study of this problem by relating the edge-connectivity of a graph, i.e., the minimum number of edges whose deletion partitions G, to its resiliency. Following the success of randomized routing algorithms in dealing with a variety of problems (e.g., Valiant load balancing in the network design problem), we embark upon a study of randomized routing algorithms for the Static-Routing-Resiliency problem. For any k-connected graph, we show a surprisingly simple randomized algorithm that has expected number of hops O(|V|k) if at most k-1 edges fail, which reduces to O(|V|) if only a fraction t of the links fail (where t < 1 is a constant). Furthermore, our algorithm is deterministic if the routing does not encounter any failed link.
|
|
