The complexity of general-valued CSPs seen from the other side

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic equivalence. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the $k$-th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.Comment: v2: Full version of a FOCS'18 paper; improved presentation and small correction

Phylogeography of the Mekong mud snake (Enhydris subtaeniata): the biogeographic importance of dynamic river drainages and fluctuating sea levels for semiaquatic taxa in Indochina

During the Cenozoic, Southeast Asia was profoundly affected by plate tectonic events, dynamic river systems, fluctuating sea levels, shifting coastlines, and climatic variation, which have influenced the ecological and evolutionary trajectories of the Southeast Asian flora and fauna. We examined the role of these paleogeographic factors on shaping phylogeographic patterns focusing on a species of semiaquatic snake, Enhydris subtaeniata (Serpentes: Homalopsidae) using sequence data from three mitochondrial fragments (cytochrome b, ND4, and ATPase—2785 bp). We sampled E. subtaeniata from seven locations in three river drainage basins that encompassed most of this species’ range. Genetic diversities were typically low within locations but high across locations. Moreover, each location had a unique suite of haplotypes not shared among locations, and pairwise φST values (0.713–0.998) were highly significant between all location pairs. Relationships among phylogroups were well resolved and analysis of molecular variance (AMOVA) revealed strong geographical partitioning of genetic variance among the three river drainage basins surveyed. The genetic differences observed among the populations of E. subtaeniata were likely shaped by the Quaternary landscapes of Indochina and the Sunda Shelf. Historically, the middle and lower Mekong consisted of strongly dissected river valleys separated by low mountain ranges and much of the Sunda Shelf consisted of lowland river valleys that served to connect faunas associated with major regional rivers. It is thus likely that the contemporary genetic patterns observed among populations of E. subtaeniata are the result of their histories in a complex terrain that created abundant opportunities for genetic isolation and divergence yet also provided lowland connections across now drowned river valleys

Detecting and Exploiting Subproblem Tractability

International audienceConstraint satisfaction problems may be nearly tractable. For instance, most of the relations in a problem might belong to a tractable language. We introduce a method to take advantage of this fact by computing a backdoor to this tractable language. The method can be applied to many tractable classes for which the membership test is itself tractable. We introduce therefore two polynomial membership testing algorithms, to check if a language is closed under a majority or conservative Mal'tsev polymorphism, respectively. Then we show that computing a minimal backdoor for such classes is fixed parameter tractable (FPT) if the tractable subset of relations is given, and W[2]- complete otherwise. Finally, we report experimental results on the XCSP benchmark set. We identi- fied a few promising problem classes where prob- lems were nearly closed under a majority polymorphism and small backdoors could be computed

Learning Constraints through Partial Queries

International audienceLearning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, we learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm, called QuAcq2, that, given a negative example, elucidates a constraint of the target network in a number of queries logarithmic in the size of the example. The whole constraint network can then be learned with a polynomial number of partial queries. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases. We provide a version of QuAcq2 with a cutoff mechanism that controls the time to generate a query. Our experiments illustrate the good behavior of QuAcq2 in practice, especially in the case where QuAcq2 is executed to learn the missing constraints in a partially filled constraint model. Our experiments also show that QuAcq2 requires significantly fewer queries to learn a network than its predecessor QuAcq1

Partial Queries for Constraint Acquisition

Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, we learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm, called QUACQ, that, given a negative example, focuses onto a constraint of the target network in a number of queries logarithmic in the size of the example. The whole constraint network can then be learned with a polynomial number of partial queries. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases