Matches in SemOpenAlex for { <https://semopenalex.org/work/W2983374966> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W2983374966 abstract "In the ${-1,0,1}$-APSP problem the goal is to compute all-pairs shortest paths (APSP) on a directed graph whose edge weights are all from ${-1,0,1}$. In the (min,max)-product problem the input is two $ntimes n$ matrices $A$ and $B$, and the goal is to output the (min,max)-product of $A$ and $B$. This paper provides a new algorithm for the ${-1,0,1}$-APSP problem via a simple reduction to the target-(min,max)-product problem where the input is three $ntimes n$ matrices $A,B$, and $T$, and the goal is to output a Boolean $ntimes n$ matrix $C$ such that the $(i,j)$ entry of $C$ is 1 if and only if the $(i,j)$ entry of the (min,max)-product of $A$ and $B$ is exactly the $(i,j)$ entry of the target matrix $T$. If (min,max)-product can be solved in $T_{MM}(n) = Omega(n^2)$ time then it is straightforward to solve target-(min,max)-product in $O(T_{MM}(n))$ time. Thus, given the recent result of Bringmann, Kunnemann, and Wegrzycki [STOC 2019], the ${-1,0,1}$-APSP problem can be solved in the same time needed for solving approximate APSP on graphs with positive weights. Moreover, we design a simple algorithm for target-(min,max)-product when the inputs are restricted to the family of inputs generated by our reduction. Using fast rectangular matrix multiplication, the new algorithm is faster than the current best known algorithm for (min,max)-product." @default.
- W2983374966 created "2019-11-22" @default.
- W2983374966 creator A5028866207 @default.
- W2983374966 creator A5049614530 @default.
- W2983374966 creator A5076616592 @default.
- W2983374966 creator A5088655952 @default.
- W2983374966 date "2019-11-14" @default.
- W2983374966 modified "2023-09-26" @default.
- W2983374966 title "{-1, 0, 1}-APSP and (min, max)-Product Problems." @default.
- W2983374966 cites W1511191949 @default.
- W2983374966 cites W1544195453 @default.
- W2983374966 cites W1569200683 @default.
- W2983374966 cites W2007572995 @default.
- W2983374966 cites W2028341270 @default.
- W2983374966 cites W2038084411 @default.
- W2983374966 cites W2072064573 @default.
- W2983374966 cites W2084803275 @default.
- W2983374966 cites W2097382431 @default.
- W2983374966 cites W2104734478 @default.
- W2983374966 cites W2114365471 @default.
- W2983374966 cites W2117946984 @default.
- W2983374966 cites W2263246245 @default.
- W2983374966 cites W2618199688 @default.
- W2983374966 cites W2898839814 @default.
- W2983374966 cites W2963464974 @default.
- W2983374966 cites W3022326557 @default.
- W2983374966 hasPublicationYear "2019" @default.
- W2983374966 type Work @default.
- W2983374966 sameAs 2983374966 @default.
- W2983374966 citedByCount "0" @default.
- W2983374966 crossrefType "posted-content" @default.
- W2983374966 hasAuthorship W2983374966A5028866207 @default.
- W2983374966 hasAuthorship W2983374966A5049614530 @default.
- W2983374966 hasAuthorship W2983374966A5076616592 @default.
- W2983374966 hasAuthorship W2983374966A5088655952 @default.
- W2983374966 hasConcept C106487976 @default.
- W2983374966 hasConcept C111335779 @default.
- W2983374966 hasConcept C111472728 @default.
- W2983374966 hasConcept C114614502 @default.
- W2983374966 hasConcept C118615104 @default.
- W2983374966 hasConcept C121332964 @default.
- W2983374966 hasConcept C138885662 @default.
- W2983374966 hasConcept C17349429 @default.
- W2983374966 hasConcept C185592680 @default.
- W2983374966 hasConcept C2524010 @default.
- W2983374966 hasConcept C2780586882 @default.
- W2983374966 hasConcept C33923547 @default.
- W2983374966 hasConcept C43617362 @default.
- W2983374966 hasConcept C62520636 @default.
- W2983374966 hasConcept C84114770 @default.
- W2983374966 hasConcept C90673727 @default.
- W2983374966 hasConceptScore W2983374966C106487976 @default.
- W2983374966 hasConceptScore W2983374966C111335779 @default.
- W2983374966 hasConceptScore W2983374966C111472728 @default.
- W2983374966 hasConceptScore W2983374966C114614502 @default.
- W2983374966 hasConceptScore W2983374966C118615104 @default.
- W2983374966 hasConceptScore W2983374966C121332964 @default.
- W2983374966 hasConceptScore W2983374966C138885662 @default.
- W2983374966 hasConceptScore W2983374966C17349429 @default.
- W2983374966 hasConceptScore W2983374966C185592680 @default.
- W2983374966 hasConceptScore W2983374966C2524010 @default.
- W2983374966 hasConceptScore W2983374966C2780586882 @default.
- W2983374966 hasConceptScore W2983374966C33923547 @default.
- W2983374966 hasConceptScore W2983374966C43617362 @default.
- W2983374966 hasConceptScore W2983374966C62520636 @default.
- W2983374966 hasConceptScore W2983374966C84114770 @default.
- W2983374966 hasConceptScore W2983374966C90673727 @default.
- W2983374966 hasLocation W29833749661 @default.
- W2983374966 hasOpenAccess W2983374966 @default.
- W2983374966 hasPrimaryLocation W29833749661 @default.
- W2983374966 hasRelatedWork W149967810 @default.
- W2983374966 hasRelatedWork W1584025548 @default.
- W2983374966 hasRelatedWork W2028009936 @default.
- W2983374966 hasRelatedWork W2048824634 @default.
- W2983374966 hasRelatedWork W2078948975 @default.
- W2983374966 hasRelatedWork W2185065513 @default.
- W2983374966 hasRelatedWork W2302499562 @default.
- W2983374966 hasRelatedWork W2503875446 @default.
- W2983374966 hasRelatedWork W2734878070 @default.
- W2983374966 hasRelatedWork W2735329691 @default.
- W2983374966 hasRelatedWork W2739024676 @default.
- W2983374966 hasRelatedWork W2883037415 @default.
- W2983374966 hasRelatedWork W2886086760 @default.
- W2983374966 hasRelatedWork W2949588463 @default.
- W2983374966 hasRelatedWork W2950394272 @default.
- W2983374966 hasRelatedWork W2950456228 @default.
- W2983374966 hasRelatedWork W2969396942 @default.
- W2983374966 hasRelatedWork W2978301121 @default.
- W2983374966 hasRelatedWork W3185628527 @default.
- W2983374966 hasRelatedWork W787742013 @default.
- W2983374966 isParatext "false" @default.
- W2983374966 isRetracted "false" @default.
- W2983374966 magId "2983374966" @default.
- W2983374966 workType "article" @default.