Matches in SemOpenAlex for { <https://semopenalex.org/work/W2898977239> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W2898977239 abstract "We consider the ILP Feasibility problem: given an integer linear program ${Ax = b, xgeq 0}$, where $A$ is an integer matrix with $k$ rows and $ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists $xinmathbb{N}^ell$ that satisfies $Ax = b$. Our goal is to study the complexity of ILP Feasibility when both $k$, the number of constraints (rows of $A$), and $|A|_infty$, the largest absolute value in $A$, are small. Papadimitriou [J. ACM, 1981] was the first to give a fixed-parameter algorithm for ILP Feasibility in this setting, with running time $left((|Amid b|_infty) cdot kright)^{O(k^2)}$. This was very recently improved by Eisenbrand and Weismantel [SODA 2018], who used the Steinitz lemma to design an algorithm with running time $(k|A|_infty)^{O(k)}cdot |b|_infty^2$, and subsequently by Jansen and Rohwedder [2018] to $O(k|A|_infty)^{k}cdot log |b|_infty$. We prove that for ${0,1}$-matrices $A$, the dependency on $k$ is probably optimal: an algorithm with running time $2^{o(klog k)}cdot (ell+|b|_infty)^{o(k)}$ would contradict ETH. This improves previous non-tight lower bounds of Fomin et al. [ESA 2018]. We then consider ILPs with many constraints, but structured in a shallow way. Precisely, we consider the dual treedepth of the matrix $A$, which is the treedepth of the graph over the rows of $A$, with two rows adjacent if in some column they both contain a non-zero entry. It was recently shown by Koutecký et al. [ICALP 2018] that ILP Feasibility can be solved in time $|A|_infty^{2^{O(td(A))}}cdot (k+ell+log |b|_infty)^{O(1)}$. We present a streamlined proof of this fact and prove optimality: even assuming that all entries of $A$ and $b$ are in ${-1,0,1}$, the existence of an algorithm with running time $2^{2^{o(td(A))}}cdot (k+ell)^{O(1)}$ would contradict ETH." @default.
- W2898977239 created "2018-11-09" @default.
- W2898977239 creator A5000479623 @default.
- W2898977239 creator A5054859737 @default.
- W2898977239 creator A5073361240 @default.
- W2898977239 date "2018-11-03" @default.
- W2898977239 modified "2023-10-11" @default.
- W2898977239 title "Tight complexity lower bounds for integer linear programming with few constraints" @default.
- W2898977239 cites W1779426617 @default.
- W2898977239 cites W1985572324 @default.
- W2898977239 cites W1995725694 @default.
- W2898977239 cites W2003979824 @default.
- W2898977239 cites W2026129593 @default.
- W2898977239 cites W2043263883 @default.
- W2898977239 cites W2090960684 @default.
- W2898977239 cites W2103658959 @default.
- W2898977239 cites W2114616381 @default.
- W2898977239 cites W2315822933 @default.
- W2898977239 cites W2326750642 @default.
- W2898977239 cites W2607993745 @default.
- W2898977239 cites W2774158340 @default.
- W2898977239 cites W2779795514 @default.
- W2898977239 cites W2930306418 @default.
- W2898977239 cites W2956842124 @default.
- W2898977239 cites W2963606510 @default.
- W2898977239 cites W3021408647 @default.
- W2898977239 cites W3103589466 @default.
- W2898977239 cites W69369304 @default.
- W2898977239 hasPublicationYear "2018" @default.
- W2898977239 type Work @default.
- W2898977239 sameAs 2898977239 @default.
- W2898977239 citedByCount "1" @default.
- W2898977239 countsByYear W28989772392019 @default.
- W2898977239 crossrefType "posted-content" @default.
- W2898977239 hasAuthorship W2898977239A5000479623 @default.
- W2898977239 hasAuthorship W2898977239A5054859737 @default.
- W2898977239 hasAuthorship W2898977239A5073361240 @default.
- W2898977239 hasConcept C106487976 @default.
- W2898977239 hasConcept C11413529 @default.
- W2898977239 hasConcept C114614502 @default.
- W2898977239 hasConcept C118615104 @default.
- W2898977239 hasConcept C132525143 @default.
- W2898977239 hasConcept C135598885 @default.
- W2898977239 hasConcept C159985019 @default.
- W2898977239 hasConcept C192562407 @default.
- W2898977239 hasConcept C199360897 @default.
- W2898977239 hasConcept C33923547 @default.
- W2898977239 hasConcept C41008148 @default.
- W2898977239 hasConcept C41045048 @default.
- W2898977239 hasConcept C56086750 @default.
- W2898977239 hasConcept C77088390 @default.
- W2898977239 hasConcept C97137487 @default.
- W2898977239 hasConceptScore W2898977239C106487976 @default.
- W2898977239 hasConceptScore W2898977239C11413529 @default.
- W2898977239 hasConceptScore W2898977239C114614502 @default.
- W2898977239 hasConceptScore W2898977239C118615104 @default.
- W2898977239 hasConceptScore W2898977239C132525143 @default.
- W2898977239 hasConceptScore W2898977239C135598885 @default.
- W2898977239 hasConceptScore W2898977239C159985019 @default.
- W2898977239 hasConceptScore W2898977239C192562407 @default.
- W2898977239 hasConceptScore W2898977239C199360897 @default.
- W2898977239 hasConceptScore W2898977239C33923547 @default.
- W2898977239 hasConceptScore W2898977239C41008148 @default.
- W2898977239 hasConceptScore W2898977239C41045048 @default.
- W2898977239 hasConceptScore W2898977239C56086750 @default.
- W2898977239 hasConceptScore W2898977239C77088390 @default.
- W2898977239 hasConceptScore W2898977239C97137487 @default.
- W2898977239 hasLocation W28989772391 @default.
- W2898977239 hasOpenAccess W2898977239 @default.
- W2898977239 hasPrimaryLocation W28989772391 @default.
- W2898977239 hasRelatedWork W2049661027 @default.
- W2898977239 hasRelatedWork W2183936573 @default.
- W2898977239 hasRelatedWork W2224152264 @default.
- W2898977239 hasRelatedWork W2274447119 @default.
- W2898977239 hasRelatedWork W2468706558 @default.
- W2898977239 hasRelatedWork W2537252502 @default.
- W2898977239 hasRelatedWork W2552717912 @default.
- W2898977239 hasRelatedWork W2775084241 @default.
- W2898977239 hasRelatedWork W2794380282 @default.
- W2898977239 hasRelatedWork W2944399784 @default.
- W2898977239 hasRelatedWork W2945408305 @default.
- W2898977239 hasRelatedWork W2949062889 @default.
- W2898977239 hasRelatedWork W2949510380 @default.
- W2898977239 hasRelatedWork W2965200911 @default.
- W2898977239 hasRelatedWork W3088630545 @default.
- W2898977239 hasRelatedWork W3107874748 @default.
- W2898977239 hasRelatedWork W3126429899 @default.
- W2898977239 hasRelatedWork W3160700943 @default.
- W2898977239 hasRelatedWork W3180912679 @default.
- W2898977239 hasRelatedWork W2155476808 @default.
- W2898977239 isParatext "false" @default.
- W2898977239 isRetracted "false" @default.
- W2898977239 magId "2898977239" @default.
- W2898977239 workType "article" @default.